What should my sister say to her "daughter" ?

My sister has been with her bf for 2 and a half years. He has a little girl who will be 2 next week. When the child was conceived it was just a drunken night and the girl was pregnant when my sister started dating him. I think it was a dumb move on her part, but whats done is done. Anyway, the little girl has always known my sister as mommy. Nobody told her to call my sister mommy, she just started doing it on her own because she saw my sister with daddy and automatically thought she had 2 mommys. So the real mother has now officially walked away. After a long battle she simply gave full custody to the father and retained some visitation. (She abused the child and children's services has been to her house multiple times) The children's services office did another report on her yesterday presumably. My sister and her bf haven't heard from the baby mama in several days and she hasn't come to pick up the little girl for nearly 2 weeks. Now they are trying to figure out how to explain things to the little girl in a way that won't make her realize that her mother abandoned her. My suggestion was to tell her that she was too good for the mommy that pushed her out of her belly so my sister became her new mommy. I have no sympathy or desire to preserve the baby mama's reputation because she walked away from her own child after abusing her!! I think that they should protect the little girl's self esteem before worrying about the baby mama's reputation! I don't know if I am thinking clearly though because I adore that little girl and I hate her mother for abusing her. That isn't to say that my sister and her bf don't hate the baby mama as well, but we all want to do what is best for the little girl. Any advice?