Hm. What is she doing that is bad? What isn't she listening to?
More information would be helpful.
why would you let her do what she wants? Children thrive on order. I know that it is hard to be the one to make the rules and inforce them, but that is what parents do. You need to be in charge not her. You can be both the fun mom and the tough mom. trust me she will thank you for it later.
I'd dump the boyfriend and focus on the daughter. Learn some good discipline methods and give her some attention also. The boyfriend doesn't have the right to tell your child what to do unless he is her father, that might be part of why she is acting up.