Dad is an endearing term. As for not wanting to see him every night, you can't let his presence bother you. Distance yourself from his actions, from him, and don't let his actions drag you down. Be strong for your mother, because she'll need you as much as you need her, and try not to hate, because hating won't hurt him, just you. I may not have succeeded in all these things, but I'm trying, and so should you.
Verbal abuse is just as harmful.
The only difference is that the deep bruising appears beneath the surface. With that said, you need to take care of yourself. If your family is too involved to offer you the support you need, turn to close friends, professionals, and support groups that can help provide invaluable insight. Just because her father cheats, doesn't mean he doesn't love her mother. I learned early that my dad cheated whenever he worked away from home.