Been there, done that.
DSD said she won't visit if I moved in (that was about 7 years ago). She wrote a few heartbreaking letters that brought me to tears, and I have experienced first hand the anger and disappointment of daddy's little girl now having "to share" her dad with me.
On the bright side? Here is how it worked out for us: her dad told her that he loves her tons, he will always call, she is always his favorite little girl, and he will always pick her up if she wants to see him, but I'm moving in. If she doesn't want to come over, he'll call to say I love yous, and will miss her, but he won't force her to come over if she doesn't want to.
When I moved in - dsd never canceled a weekend (not saying it will work that way for you, but it did work out for us).
We had lots of friction, but when I left all parenting to DP, a lot of it smoothed out between dsd and myself. We are in a fairly good place right now. She is 17 now, and for three years has been living with us, from her own choice, by her own request.
13 was rough all around.
#1. Disengage. From everything. Don't talk to her, don't address her when she is being rude, allow her dad to manage it. Walk away from arguments.
#2. Stick to the mantra "I love you, but I don't think we can talk right now."
#3. Tell your bf that he has a choice to make, and he is quite free to make it. However! Please realize, the less sure he is of what he wants, the more his daughter will sense it and use it to her advantage. Until you know he is ready for this step - don't move in. The two of you have to be a unit for the blended thing to work. I doubt that excluding you from dsd's life to satisfy her sadness is the right way to go. It will feed into it, give it more power, and will make everyone, including the daughter, miserable.
#4. Realize that you might have to start over with the daughter, and realize that it's okay. Don't take things personal. If you are treating her with love and respect, she really has no reason to dislike you. You just need a new approach. Things CAN change. They did for us! It went from okay, to bad, to SUPER bad, to okay, to pretty good! I'm the one she drove on the highway the first time with, I was the one to hear about her first kiss, and I was the one she's going out for ice-cream with in 30 mins. We were in a pretty rough spot when she was 11-13.
#5. Discuss this in detail with your bf. How it breaks your heart, how you feel his resentment, how you are lost, how you don't want to be part of a family where you are excluded, how you need to be a couple and co-parents, and have a strategy on working with each of the children involved here.
#6. Try to connect with dsd. Slowly. Look for the right moment, look for the right opportunity, PLAN to make it happen with your bf. find something she'd have hard time saying no to - going to a brand new place (big city nearby?) just for a girls day out? taking her to some store she never gets to go? Play it cool if she says no, and be creative. One time she will bite - don't say much, let her lead the conversation. Then repeat. Those are the silly outings that help to create a bond, but it woudl have to be just you and her.
#7. Don't take it personal when she wants to spend time with her dad. Help them create a ritual just for the two of them. Maybe it's going to the coffee shop every Sunday morning, maybe it's going for a walk, but help them find something that will help her feel more secure.
And of course, come back here and share your ups and downs.