My uncle had a stroke around 7 years ago, he too had to depend on the people around him. He was in a wheelchair, speaking was difficult, he had to be fed, cleaned, dressed... everything. He too had periods of behaving in a similar way. He hated the fact that it happened, and that his family had to care for him in such a way. He would get really frustrated with everything. At first my auntie had people in to help usually in the morning, and in the evening. They would help out with some of the daily tasks such as taking him to the bathroom, cleaning him, putting him to bed and such. This made things easier for my aunite, but at the end of the day, even with that help she couldn't cope. He now lives in a home, has full time care, and though he still has his moments, his mood has improved.
If you are finding it difficult to cope at home, maybe having someone in to help with the care of your father will make things easier for you. Sometimes it doesn't work out, but sometimes it can make a huge difference in the home environment. It takes a little weight off of your shoulders, but it also gives your father the chance to stay at home, and be with the people he is closest to.
Another option, which people don't particularly like, but sometimes they have no other choice, is full time care. It's a very difficult decision to come to, putting someone that you love in care, but sometimes it's the best thing for you, and them. They will receive the best quality care and the family can get at least some normality back into their lives.
Unless you have experienced something like this yourself, you'll never really understand. I can't imagine what it must be like for you at home, and I can completely understand your anger, and your frustration. As a family, you don't seem to be coping and it's important that you talk about it, and maybe do something about it. It's difficult, no doubt about it, but you, your mother, and your brother deserve a life too, and right now, you don't have that. I think it's important that you at least try, if you haven't done already, some outside care and see how it goes.