I have a ??? Its a bit long please helpful advice

My husband has a 6year old daughter who is very intelligent and aware of everything. He and the mother have be broken up since 2012 .the mother has a new man now since then she has accepted islam she lives it but not in every way from what i can see. She has never had a job since the child was born. She supports her self with govenment assistance.she lives with her man but he puts her out every couple of months.  We know this because the child tells us how he hits her mother and how shes bleeding and has a black eye on a regular basis . He is a convicted felon also . He also does not have a job. she is back n forth with the child from her mothers house she and her man live in a drug infested neighborhood with drug adicts on every corner on all times of the night ive seen it with my own two eyes  . We have heard heresay of her being seen so high on some kind of drug that she could not even stand. Thats just here say we have no proof. She and my husband are now in court proceedings over custody after she restricted him from picking his child up. In court she attacked him with a knife now he has a protection order against her. Her reasons are we dont practice islam and for that reason our home is not structured enough for the child.( in her written text from the court order)  We both have great paying jobs and  1 car each .we live in a gated community our home is in our name he does pay child support but he does not give her actual money he just buys what ever the child needs. Can religion trump my husband wanting primary custody for best intrest of the child. She is her mother but she does not do the things a mother should do 100% of the time it seems that she does certain things when she sees we are doing them the child was with both parents for equal amount of times untill she sent her looking messy and dirty. I then re did her hair the same exact way her mother did it nothing different i just refreshed it and put new clothes on her the clothes she was sent in were old and dirty looking .(side note) she always sends the child that way and as a woman i feel like i have to present her like a little girl .after that this whole thing started . we do not talk about adult things in front of the child. we teach her, read to her and help her with school work and make sure shes washed fed and to school on time . and because i want to be a mother i try my best to do the best for her  her father works so hard to get her every thing she needs .i think the mother feels as if im trying to replace her or something but i let the child know i love you as if you were my own but i am your step mother not your mother and i feel like  she understands that  she calls me by a nick name she gave me not mom i would not condone that . why does the mother  choose to act this way?  are we wrong for feeling like she should primarily live with us or is that too much? .we dont want to take her from the mother but we both collectively feel she needs time to get on her feet so she can take care of her child the way she needs too