You aren't giving anyone enough information to be able to help you, here.
Does biological dad WANT you to move in with him?
Do you have anything beyond a Birthday and Christmas "idealized" relationship with him?
Does he have another family?
If you don't really know your father, don't pin your hopes on him doing the fairy tale "Ewwwww, come home darling daughter, I'll PROTECT YOU!!" nonsense. He'd have been there before now if that were the case.
Have you ASKED him about this? Does he know your situation? Be careful--he may just call Child Services and "solve" your problem by getting you slapped into foster care.
You have several choices before you.
1. You can call 911 the next time MOM kicks your ahhss. Make sure you're wounded, though--the police want to see bruises. And make sure you aren't hitting back, either.
Keep in mind you could end up in foster care, and your mom could end up in court, jail and probation.
Oh, here's a tip for you if she starts hitting--run out into the front yard or the street (if it's not too busy). Yell, "STOP HITTING ME, STOP BEATING ME!!!" at the top of your lungs. Funny how people worry more about what the neighbors think than what their own FAMILY thinks of them.
2. You can sit MOM down and tell her, straight up, that if she lays another hand on you EVER AGAIN, that you WILL report her to the police. You don't give a rat's ahhs if she was beaten as a child--that's NO EXCUSE. Tell her that you PROMISE if she hits you, you're reporting her to the police. She'll go to court, you'll go to foster care. Tell her you MEAN IT. And then, follow through if you have to.
3. Her relationship with her husband isn't for you to resolve. She made the sheety deal, she's stuck with it. If you come across compelling evidence of cheating, like say, a video, or a voicemail message, pass it on, but then back off. She probably already knows she picked a loser--you're just rubbing it in.
4. GO TO YOUR ROOM. For the next two years, when you're not at school, at after-school activities, at your part-time job (don't have one? GET ONE. And start a savings account--you'll need it for when you MOVE OUT), or staying over at your best friend's house, GO TO YOUR ROOM. Make your room as comfortable as possible, so you don't have to leave it. Get a mini cooler for drinks, and put your snacks in your sock drawer .... and keep it clean and cozy. Stay OUT OF THEIR WAY, particularly when StepDad is drunk on his behind.
5. When you're eighteen, either get gone to college (study hard and apply for scholarships; supposedly this Obama fellow is going to loosen up student loan opportunities too) or find yourself a full time job if you're not an academic lightbulb. MOVE OUT. Start your own life, even if your first apartment is just a tiny studio.
I wish you luck. You're in a crummy spot.
You might want to join Al-Anon/Al-Ateen (support group for families/teens with alcoholics in the family--they can help you with coping strategies--see the link). You might make some friends and get a few ideas as to how to manage your life living in that dreadful chaos.