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No you can not ask the courts to force the mother to take her. In fact as much as you do not want to hear it you have very few rights as far as this child is concerned. Her father must make the choices on what to do with the child and even he can not force her mother to take her. If he has custody he must deal with his child or ask the courts to remove the child and place her in foster care.
Your only option is to either force dad to deal with his child or leave. You can not make him deal with her nor can you make mom butt out unless dad tells her to. Mom has a right to talk to dad and the child about child rearing even if she is not the custodial parent.
It sounds like your husband needs to make some real choices real quick with his daughter. If he fails to do so you have the right to leave or divorce him.