I personally don't think this situation can be worked out. She is a minor and not a very old one at 13. A lot of years left for her dad to be actively in her life (and he clearly needs to be) and this will continue to get worse as time goes on. Your boyfriend is a packaged deal with his daughter. That you two fight over it means that he is not seeing your side or feels stuck . . . either way, it means it's not going to stop. Sometimes packaged deals work out and sometimes they just don't. Like dating . . .sometimes relationships stand the test of time and other times, they do not. And that is supposed to be the way it works. We have to pick the best situation for ourselves in life and this isn't the best for you or your daughter.
Save yourself and move on from this man. And don't make him feel bad for it because he NEEDS to be a dad to her. She may have some emotional problems or mental health issues, I don't know. She's a young teen (not a charming age to begin with) and clearly has a problem with you. It's not going away. And you can't ask her dad to choose as that would be the wrong thing to do. So, cut your losses and have a more peaceful home with you and your daughter (minus boyfriend and his).
Just my opinion, of course! Good luck