You said you go to court in 12 days. Though I know nothing about custody battles it seems to me that you should also discuss these incidents, and the fact that you are making a child abuse report, with your lawyer. If this man is abusing his daughter he should definitely not be given custody!!!! The lawyer may also be able to advise you on next steps.
I also forgot to mention above that when you call Child Protective Services you do not automatically have to file a report. You can talk with them first about what you have seen and heard and they can advise you on whether a report is necessary. This can all be done anonymously if you wish. However, based on the little you have said above I would not hesitate to report it. Your actions right now could be life-changing for this girl. Abuse robs the abused of a voice, especially when the abused is a child, as is evident in her silence on the matter. You (and/or her mother) can speak out for her until she is in a position to gain her own voice back again.
I am a teacher of young children and so this issue is very emotional and personal for me, having seen the effects of abuse on children I care deeply about. Whenever I am not sure whether to take action, I ask myself how I would feel years later if I found out that abuse was taking place and I had not done anything to try to stop it. The worst (well, best!) that can happen is that you are wrong.