oboy, been there!  First and foremost, do NOTHING that places you between your man and his child, because you - will - lose.  Profess to be her friend and try to some extent to develop a relationship with her - take her out to dinner at a nice restaurant and find out what is on her mind, etc., take her shopping, etc. - however do not expect that this will fix things, because she undoubtedly sees you as an enemy and even may be wanting her parents to get back together.  Over time, if your relationship with her father is strong and supportive, she may very well come around to accept you as a friend.

I contribute these thoughts because my husband of 23 years has a daughter who was a teen when we met, and she turned out to be a piece of work.  She's in her thirties now and I believe that she secretly still thinks her parents will get back together - how sad.  I feel for the kids of broken families and the pain they live with.  But some - like his two sons - adapt and thrive with the new relationships, and some don't.  You just don't have much control over this.