All parents fight amongst themselves just as those around them do. What’s important and crucial to them is tedious and cumbersome to those around. Now granted that this is not the fact all the time I’d say that if you, your sister, and mother approach your father about this he’d be outmatched. Remember you have to have respect for your father and your mother both, but there’s a difference between respecting the ones you love and informing them when they are wrong. If he is easily angered, like my mother, then tell him that he shouldn’t get so mad about every little thing and that if we wanted your opinion we would have asked for it. Your two cents are appreciated every once in a while, but you don’t need to make a habit out of it.
It can be difficult for you to tell him this, like it was for me to tell my mother the same thing, but remember unlike me who had to scream my own point across for it to sink in, you have a sibling and a parent on your side to make sure he can’t take it too far. I’d say it’s best to approach your mother first about these facts you have both notice together; putting an emphasis on together, so it doesn’t seem like it’s just your single opinion. Remember, no one single person can change anothers mind, especially if that person is a stubborn old bullheaded know-it-all, but with even one extra person it makes the “Real” facts become so much more apparent. Not only that by doing this, it distills courage for you and others to do the right thing, rather then pent it up and let it get worse. It also gives you point pf maturity in the persons favor despite how angry he may get about hearing the facts.
A wise person once said, “Humans naturally want to hear words that they wish to hear even if it means casting themselves into an illusion of false truths, but it takes true courage to cast aside the false truths and accept that which you can not.”