Moth Feathers
Actually, inappropriate elimination and vomiting can be signs of serious issues going on.
First, is her cat spayed?
Second, has she been to the vet to rule out any urinary tract problems? It's very common in cats, particularly when they are fed dry food, and if the problems aren't treated they can lead to much worse maladies.
Third, how many litterboxes are in the household? Sometimes cats will protect litterboxes from other cats in the household. There should be one litterbox per cat plus one extra, so in total you should have three litterboxes.
What kind of litterboxes are they and what litter do you use? How often are they scooped? Some cats don't like hooded litterboxes, and some can be picky on the litter. Litterboxes should be scooped at least once a day.
For the vomiting, are the cats free-fed? Freefeeding can contribute to that. Also, feeding a high quality diet should help significantly with the vomiting, if not eliminate it entirely. Many cats have allergies to the grains and other nasties put in low-quality cat foods.
Beat me to it. The only thing I would add, is if she is a long haired cat or an excessive groomer she may have issues bring up hairballs. Also, if she is having issues getting rid of the extra hair, that could be contributing to her inappropriate elimination habits. If she has a blockage or UTI as Moth mentioned, she will avoid the box as she associates it with the pain of attempting to go.
Also, make sure she isn't eating anything weird. I had trouble with one of my cats who eats plastic bags and then it hurts when it comes out the other end. Only solution is to be hyper-aware of where you leave the bags.
As for the number of litter boxes... depending on the cat you may need more boxes than Moth recomended. Two of our cats don't mix their pee and poo, so we need four boxes just for them, plus 3 more for the other two cats. Total of 7 boxes for 4 cats. Also we found for the ones that don't mix their locations, they liked to pee in uncovered boxes, but poop in hooded boxes.
Finally, what kind of litter is being used? Most cats hate the dusty-grossness of clay litter, try switching to corn or wheat litter. World's Best and Swheat Scoop are two brands I like. Plush they are flush-able is a plus.