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1.) I'm only nervous when I canter her. And I don't canter her often. The video was the first time I had cantered in probably a year or just slightly less. Honestly, I've gone through so much with this horse that I'm the ONLY ONE who can get on her back without her having a hissy fit.
I can tell you right now, I feel your pain. My trainer has a Quarter pony mare and she is a PAIN IN THE a**. I will admit, she is much worse than your horse and your horse is an Arab mare. Your pony is an angel compared to mine. I too, am the only one that can ride her, because I'm the only one that has the patience. So, even if you haven't cantered in awhile, you still have to work up to it.

2.) As I said, I was never taught which diaganol to trot on. I'm trying to keep it in my head to rise with the outside. Right?
Close. You have to rise to the inside leg.

3.) Mkay, I can understand how that would keep her head up. But she isn't, nor has she ever been head shy. She was at one point refusing the bit (When I first got her) because she was abused and didn't want her ear touched. She'd been tied by her ears.
Anyway, I'll lower my hands.
We said that she can BECOME head shy, if the bit is being pulled too much or if there is too much tension through the hands and arms. My pony I am training (mentioned in answer 1), was also tied by the ears and I have a hell of a time getting the crown piece over her ears and then that spooks her and gets her riled up and then my ride will be all over the place. With a horse like that, I would do A LOT of trotting as a warm-up until you can trot her at a steady, forward pace, with the reins lose and held only at the buckle.

4.) I've been working on my seat for as long as I've owned her. She is the hardest horse to work with simply BECAUSE all she wants to do is go fast.
Read above answer. A lot of hard trotting and firm halfhalts should help your pony learn a steady pace. And if she is smooth enough, try a good 30 minutes of sitting-trot.

5.) Before giving the aid to canter, you must SIT three strong beats, preferably using your back a potential halfhalt to, three beats are minimum, but as our training, our trainer made us go over an hour lesson ONLY sitting trot, NO posting.

6.) Okay. How do you expect me to get her head down, when I've had her for 5 years and her head has dropped.. five times while I was riding? Throughout the course of the 5 years? I'm exadurating, but it's true that she does not drop her head very easily. I'm aware that her head needs to be down, but it really isn't as easy as you expect it to be. I try to make the adjustments, and it only makes her crazy.
We were only trying to help and we are sorry if that came out rudely on our part. We understand. The aforementioned pony I am training is the EXACT same way. I would try the advice I gave on 3.). Having a light hand and lose reins (WITH CONTROL) will always presuade them to reach their head down. Once they do, don't try cantering. Just keep in the same, steady trot for another 10-15 minutes or so. After this is becoming a habit, try gathering up the reins inch by inch for more of a collection through the neck muscles.

7.) First of all, I don't kick her into it. I barely give her any pressure with my legs when I ride. I NEVER kick her. Ever. 'Assuming I have gotten her head under control'? I'm sorry, your critique is fine and dandy, but you're very discouraging.
If I use a whip, no matter how light the tap is, how little I use it.. Ruby will explode. I have used that kind of aid before, my old trainer was a dressage trainer, and it does NOT work with her. I don't know why people expect it to work with her when all it does is make her worse.
We did not mean "kick" or "beating". Sorry again. We just meant that you should not use hard persuasion. Again, my pony does not like the whip. I find that giving her a strong, over-corrected canter aid from the collected TROT works well. What we meant by her head being under control, is that is should be down and calm. If you don't want to use a whip, don't. Try using many methods and see what works best.

8.)Did you think that I told her to suddenly change direction? (I know they're cavaletti's btw) I didn't tell her to change! She did it herself, and I was trying to keep her from doing it!
Again, sorry for the apparent rudeness. Anyway, even if your horse did change her direction on her own, you should have have pulled her back around through the jumps and continued your ground work on that side of the jumps, NOT letting her do it again, until she got the picture. I know that having a horse that is so fidgety and unpredictable can be tough, but those are the horses that need the most bossing around. Don't be afraid to get rough and tell her how it is done. But always give her a lot of praise if she does something right, even as simple as turning her ears back to hear your voice.

9.)I realize that the arena is dressage show material, but I don't ride dressage. Don't say that the horse could care less about the fence. You don't know my horse. Ruby has taken me out of that arena so many times just at a trot. And I honestly don't care about how you can get your horse in a field with no fences. I can't do that.
And I know I'll be able to do it. Eventually.
I have never known a horse to care about the height of an arena fence. What bothered me is that you let your horse do something so entirely rude and let her get away with it. I don't care how many times you have purposely let her trot over fence out of the arena, it is still bad manners, Dressage or not.

Agn, sorry for any rudeness, we were only trying to help you out. I have been through this and the pony I am training is SO MUCH like your Arab, I think maybe I could help. But I will try not to be snooty about it, that was NEVER my first intention anyway.

Who in the world taught you that?
I mean no offense to your coach, and maybe we're just miscommunicating, but that's wrong. We always teach our little kids the rhyme "rise and fall with the leg on the wall". You rise as the outside front comes forward and you sit as it comes back. So I suppose you are rising with the inside hind, but that's harder for most people to think about. It's usually easier to think about the front legs, especially as you're learning your diagonals.

And now, for an Aria tangent on posting diagonals
Traditionally, we are always taught to post on the outside diagonal, which means that you are in the air and off of your horse's back as the inside hind comes forward. There are many different reasons for this, the most common one cited is simply tradition. As far as actual purpose in riding goes, however, the reason you rise with the outside diagonal is to allow for more freedom of movement in the inside hind. With your weight off of their back, you won't be restricting their movement at all (of course, ideally your seat should not restrict their movement in general, but people aren't perfect and that's why we post) with will allow for greater reach with the inside hind and improve the horse's gait as well as allowing for more suppleness in the bend.
Diagonals, however, are a tricky thing. Traditionally, you post on the outside diagonal for the above mentioned reasons. HOWEVER, there are many cases where posting on the "wrong" diagonal is a legitimate training exercise.
If you have a very secure, independent, and effective seat, posting on the inside diagonal (so you sit as the inside hind comes forward) can give you more control over the inside hind. This can be useful if you're working on the beginnings of collection but your horse isn't quite ready for the sitting trot yet. (more on my beliefs about the sitting trot later)
Lateral work is an area of contention when it comes to posting diagonals. Personally, I prefer to sit when I'm leg yielding because it makes it easier to get the timing right, give me more control over my horse's haunches, and in general, is just easier for me. But not every horse is ready for that, and since leg yielding is one of my favorite suppling exercises, I often have to post in the interest of the horse. There are two different schools of thought as to which diagonal you should post on when doing lateral work. For the purpose of this discussion, let's assume that you are leg yielding from the quarter line to the wall on the long side of the arena, that way "inside" and "outside" can stay consistent.
One school of thought says that you should continue to post on the outside diagonal when leg yielding because the inside hind needs that extra freedom as it crosses under the body, which is what provides the suppling part of the exercise. Again, your weight is off of your horse's back and you are therefore not restricting their movement.
Another view is that you should post on the inside diagonal when leg yielding because it improves your timing. You need to be applying the leg aid as the inside hind is lifting off of the ground, and it is much easier to apply said leg aid when you are sitting. So you can get into a rhythm where you apply the leg every time you sit, which signals the horse to swing that inside hind under their body and move sideways.
Both are correct.
The only difference is what each individual horse and rider needs. Young or inexperienced riders, I'll often have post on the "wrong" diagonal so that they can learn the timing. If I'm working with a young horse learning the movement, however, I'll usually stay on the correct diagonal because I have more precise control over my aids (although far from perfect, I have a lot of work to do) so I can focus more on improve the freedom of movement in my horse.
So, the point is, that there is no "right" or "wrong" diagonal. It all depends on what you're trying to accomplish. Posting on the "wrong" diagonal will not injure your horse unless you are twisting really hard or coming down hard on their back, and that will hurt them no matter which diagonal you're on.

Alright, next topic. The sitting trot.
A trend that I hate to see in a lot of dressage training (and I'm guilty of it too, back before I knew better) is sitting too soon, or pushing riders to sit before they and their horses are ready. You cannot sit on a tense back. You cannot sit on a hollow back. You may physically be able to, but you will not have the unity that you're looking for. The whole purpose of the sitting trot is to allow for greater precision of the aids and improved communication through the seat. If your horse is not relaxed (my definition to follow) then it doesn't matter if you glue your jeans to the saddle, you're not going to get a good sitting trot. It has nothing to do with practice, it has everything to do with preparing the horse's back to sit on. Relaxation is the state in which the horse is most willing and able to accept the rider's aids. With a high strung horse like Ruby, this means that she needs to slow down and, literally, relax. But if you have a slower, pokier horse (often seen in older quarter horses or your stereotypical "school horse) then you have to light a bit of a fire underneath them before you achieve relaxation.
Where was I going with this? Oh, yes, I remember now. Sitting trot.
Your goal is to get your horse working over their topline with a relaxed and swinging back, reaching under their body and carrying their weight in balance. Most horses move with a hollow back and a high head for two reasons (which are often related) 1) poor balance or 2) pain. Neither of these problems are helped by the rider grinding their seatbones into the horse's back and bouncing on them. If the problem is balance, suppling exercises are your friend. Leg yielding, as Brat suggested, is perfect. Lots of serpentines, figure eights, circles, and transitions both between the gaits and within the gaits, will help improve their balance. If the problem is pain, then trying to sit on them REALLY won't help, and you may want to consider a chiropractic evaluation as well as checking your saddle fit. Watching Ruby go, she doesn't look like "pain", she looks more like balance.
I know a lot of people will disagree with me when I make this statement, but I urge you, DO NOT sit on your horse's back until they are able to bring their back up and work over their topline, and until they are evenly supple throughout their body. If you bounce on your horse's back, it's only going to create more tension.

Okay, so the biggest obstacle when you have a horse like Ruby that has always carried themselves high-headed and hollow in the back, is that all of her muscles are developed for carrying her that way. Even if she suddenly had an epiphany and decided that she was going to collect herself and bring her back up and do everything perfectly, she is probably only physically capable of carrying herself like that for a few strides. Collection is HARD. It's like lifting weights. It requires a high level of fitness on the part of the horse and proper development of their musculature. Next time you're out at the barn, look at the muscles in her neck. I can't really see in the video, but I can be about 90% certain how the muscles are going to lie. Where is the largest bundle of muscles? Where does she look weakest?
Lets look at some pictures.

This horse is a dressage prospect. Look at his neck and topline. See where the muscular definition lies? The muscles are heavily developed along the top of the neck, and there is little definition along the bottom. The muscles along the bottom of the neck are the "pulling" muscles, they're the ones that allow her to yank the reins out of your hands and pull you out of your seat. The topline muscles are the carrying muscles. Those are the ones that allow a horse to lift their shoulder and move in balance with a soft and supple back.

Here's another one. The definition is not as apparent because he's not being flexed for a pose, but you can definitely see where the muscle is more developed along the crest and the topline.

This is Idocus. He's a very pretty boy with some very nice muscling.

Here you can see him in work and you can see how those muscles are used to help carry him.
This horse has a ewe neck, or an "upside down" neck. You can see how the muscular definition is mostly on the underside of the neck. This allows the horse to carry their head higher and hollow their back while pulling like hell and bracing against you.
a less severe example, but you can still see the poor muscle definition.
It's a lot harder to find horses with bad conformation that don't look beaten and abused.
The nice thing about a ewe neck, is that, for the most part, it's correctable with proper training, conditioning and development. These horses may never be Olympic dressage horses, but that's okay. They can still improve their muscle definition and become better riding horses, more pleasurable for both the horse and the rider.
There are LOTS of gadgets and training aids available to help you "get the head down". Some of these products are better than others. NONE of them should EVER be used without the direct supervision of an experienced and knowledgeable professional. It is very easy to do serious damage to your horse by not adjusting or using these devices correctly. Lunging in a side reins is often a key component in conditioning for me as it helps the horse develop the muscles that they need in order to carry themselves and respond to my aids. It is not EVER a substitute for good, solid training and it should NEVER be seen as a "shortcut".
Different people have strong opinions about different items. I am very strongly opposed to draw reins, myself, because I have seen them so frequently abused, but I do know people who can use them effectively in the right circumstances. But I can name at least four horses off the top of my head who were ruined by the improper use of draw reins. The same can be said about any training aid (although draw reins are the ones that I see most often abused and most often ruining horses) which is why it is ESSENTIAL to not experiment on your own!
The other thing that can help with this is the bending and suppling exercises. As they get the horse to release tension in the back, they will naturally stretch their head and neck down. This is NOT the same as the horse ripping the reins out of your hands and "rooting" or "diving" their head down.
Here is a horse correctly stretching down into the contact.
I saw Ruby grab the reins and dive a few times in the video you posted, so I think you know what I mean when I say that.

Okay, what else did I need to talk about? Or right, the one-rein stop. If you have her where she can flex easily at the halt, awesome! You're going to do the exact same thing at the walk, but make sure that you have NO LEG on her at all. This will be a test of your balance as she spins in a little circle. She will do this at first. Be persistent. You want her to know that this means "stop now". Keep the pressure even and consistent. Horses look for ways to get out of pressure and relieve it. When she realizes that spinning isn't working, she'll try something else. As soon as she tries "Stop and soften my neck" as a possible answer, drop the rein, thus releasing the pressure and tell her what a wonderful brilliant perfect mare she is. Then repeat. Depending on how stubborn she is, it might take a while before she gets it. Don't try it at the trot until you have it perfected at the walk. And like I said, don't practice it at the canter. It won't be a smooth transition from the canter, it will be your emergency brake when you NEED to stop because you're in danger.

Out of curiosity, have you tried riding her in the open? I know this might sound crazy... but Corky was horribly ring sour. He would be bracey run away and ignore my aids a lot more in the ring, and we would have to take a good 30 minutes of steady, easy warm up before I could have him in a place where he could easily work. But if I took my "crazy" horse out in the field, we'd have a perfect ride every time. Usually better if we were bareback because he wasn't associating it with work. May not work for her, but it's something to think about. Something as simple as removing the stirrups from the saddle made all of the difference with him, but he was kind of a special child.

Am I forgetting anything? Any other questions? Have I completely confused anyone? I sometimes think that my thoughts end up incomplete on these because I get distracted by another idea that I think is also important.

Forgive me, but that post had to go buh baii! It was getting too long and cluttered. ^-^
Anyway, as a reply, I think you will go far as a trainer for Ruby. Sometimes, our fear gets the best of us because it is easier to feel than courage is, and when fear takes us over, we forget things that we know we can do. We just panic and sometimes, freeze; mentally anyway.
I used to be like that with Hannah, but the first time she through me off (she was so abused from her previous owner, that she will start rearing and ducking out form under you if you get her ANYWHERE near a cavaletti; it's pathetic; I'll get a video of us working soon), I was so mad and embarrassed (first time she threw me off was 7 months ago), I have not let her throw me off again.
I am not too big into showing either, but my horse Mario (see sig.), was for sale and the people who were going ot buy him broke his ankle and it will take 6 months of therapy to be good agn, but they screwed him up so badly, the damage will be somewhat permanate so I'm basically out a PERFECT eventing horse. -_- I cried when I was told the news. I love my baby...
5 years and it comes to this...
Sorry, this is an emotional topic for me *shuts up*

The incident with Mario is what has made me so entirely picky with cantering....

So, the potential buyers were going to sign the buyers form that day, but they were doing a last ride. Well...they were cantering him in a 20 meter circle and the reins were too lose so his head went way down and they were forgetting to give him halfhalts so with no halfhalts and a lose rein he was just going faster and faster and faster and they had to turn him tighter so he would stay in the meter circle at such a pace and then next thing you know, they twisted him too hard and too fast a pace and then BOOM! He was lame. Unusable for 4 months, 6 months therapy and still never going to be the same.

And thank you. I take much pride in our jumping. I hate Dressage to death and I refuse to ever do Dressage with him. He is FABULOUS at it, but I'm not. But I'm training to get to Advanced jumping. Like the high Stadium jumps you see on TV. I train for that.

I really hate to cut you short, but all of the barn members are getting together in a few hours and meeting at our barn for a huge sleepover and ride-day. So, I really hope Ruby does alright (give her a treat for me), and I will have to talk to you some time tomorrow night. Bye!