Step parent adoption

I am married and my husband has custody of his 4 year old daughter. birth mom left child at 3 mos old. had no contact with child until child was year old. visits are very few and child doesn't know she is her birth mom. i have been the only mom she has known, i came into the picture when she was almost 4 mos old and have been with them ever since. is there a way to terminate the birth moms rights and able for me to adopt her? my husband and i both wish for this. he also has two other children with this woman who are now age 10 and 12 and she has them for visitation, weekends and overnights when it is convient for her and this too is very rare. we do not approve of her lifestyle of being a lesbian either. she has never taken our 4 yr daughter on any visitations..she only see's her for a few minutes when picking up or dropping the other two off. she has never asked to take our 4yr for a visitation time either.