Question about child custody?

I am the stepmom of an 11 yeaqr old girl. My husband won custody of his daughter when the child was abt 5 months old. We have been married for almost 5 years together for 10. Lately we have had some behavior problems with daughter. She has been lying and stealing from us over a period of abt 6 months. My husband does work nights and a lot of hours so I am the one usually home with her. I should mention that the mother has been pretty inconsistent with her daughter. She would skip visitation, treat her differently than other siblings, making child feel guilty for not living wth her, talk bad abt my husband and I (especially me). The past few years the mother has been more consistent and we thought things were doing better. However her daughters bad behavior started and my husband and I have been struggling to deal with it and nothing works. We have tried grounding her, rewarding her, her, taking her things away...she's still behaving badly. So fast forward to now and daughter has all the sudden been telling us she wants to live with mother. That why she is acting up is because she wants to live there. And apparently her mother has told her she is filing for custody. So we are of course worried abt the possibility of her getting custody. We do not think the mothers house is the best place for her. I want to know how much chance does she have of winning?? The mother is trying to say that her behavior problems are our fault, that she should have her. The mother is saying I am mean to her and yell at her and she shouldn't be with us anyways because her father works al the time and the child shouldn't be raised by me. So please and opinions, advice, or input would be appreciated.