What you describe is what I call a "pseudo relationship", that is , a "fake" relationship. You are sleeping in the same bed and have a daughter together but there is no relationship. If you don't talk, don't share your lives in any real way, don't even have sex, this is not a relationship. If you still have feelings for her it's worth trying to communicate. Of course, from what you say it sounds like you won't get to see your little girl if you leave, that's tragic for both of you. So maybe it's worth your attempting to get some therapy to see if you can open up some real communication. You don't say if you are married but I'm sure she will get child support if you don't get custody. (Which it sounds like you should try to do).
BUT start with trying to find some empathy for HER. She is trying to have a relationship with a mother she didn't know growing up. If you express to her that you understand why she would want that, and own up to that it hasn't been easy for you to let her mother be such a big part of your lives, then maybe she will be more open to hearing and respecting your feelings, too. But it is really important for you and the child for you to try to get some counseling whether the relationship ends or not.:o