I need advice about child support..people with knowledge please read!!?

Ok so I'm trying to take my babys father to court in order to get full custody for our daughter. He said that he wants partial custody (which I DO NOT want) for my reasons. The only thing he has against me is that I live home with my mother and grandmother and we argue and bicker every once in a while. Also that I don't have my own vehicle. But I do have 2 jobs. What I have against him is that he hit me in my jaw and drug me out the house when I was 3 months pregnant. I went to the police station and reported that incident so I have it on file. If I show the judge that doent, would that be enough proof that he isn't a fit parent and that he can't have partial custody? What about my issues, would that prove that I'm an unfit parent cause I don't have my own house or vehicle? I'm stuck between a rock and a hard place right now and really stressed out....