I believe your wife is right about being friendly toward her. Parents are huge influences on their children (for life). My wife is still struggling with issues do to her absentee father. So it's not a matter of who is more important (mom or dad) or who is the better parent. It boils down to married or not what is really best for the children are cooperative parents.
You have every right to express anger at your wife for the things she has done to you and you need to make sure she understands how important you are to your daughter and that she needs to honor her responsibility to show you respect to your daughter as well.
As far as winning her back. She has to give you the opportunity to. Realize that changes you make need to be improvements to yourself not concilatory gestures. If you don't believe in your changes, then they won't last. Also change is a two way street, both people contribute to problems in marriage, so both need to recognize their responsibility and changes that they need to make.
Sorry, lately I've been sounding like a total know-it-all jerk when in reality I am struggling as much as the people I respond too. I'm really expressing things I know I need to do as well. I just wanted to add the disclaimer to let people know I realize the flippant things I say are so much easier to say then do.