My daughter hates me. Refuses to come over. She has asked me to stop trying to stay in communication with her. She has accused me of choosing the woman I’m dating and her daughter over my own children.
My ex could have written that exact paragraph about our 16 y/o daughter. Taking you at face value that you really are a great father and did absolutely nothing to deserve her anger, I'll skip to letting you know what hasn't worked with regard to him trying to get back on her good side.
The thing that I think is most frustrating for my daughter is that dad isn't taking no for an answer. If she doesn't want to communicate, you need to back off. I imagine you are worried that she'll feel even more abandoned if you pull back entirely, but in our case, every time dad reaches out it just reinforces that he thinks his feelings are more important than hers. On this end, I can observe her softening to the idea of seeing him, then brother will pass on a message and then it is back to square one.
What I think is confusing is that the more dad tells her how very sad he is and how very much he wants to see her, the more she resents him. She looks at it as dad reversing the roles where she is supposed to meet his emotional needs and not the other way around.
Be careful that you never, ever suggest you won't pay for something if she won't see you. Our daughter not incorrectly interprets any comment such as 'Why should I pay for XYZ if you won't see me?" as a threat. He did not give her a gift last year because she wouldn't see him on her birthday, which was unbelievably painful and quite possibly the most damaging of all the things he's done. The flip side of that of course is not to bribe her with things to get her to see you or reward her if she does.
It is hard not to bring our own experiences into the discussion, so I have some advice with regard to your new girlfriend. Make sure you never, ever, ever cancel/reschedule time with your daughter in order to see your SO. Do not speak ad nauseam about your SO. Do not insist your daughter meet or spend time with your SO. Do not - for the love of God - refer to her as 'your new mom'.
Over the four years since he left, our daughter has had several stretches of blocking him out, and each time she has randomly come around on her own. She'll come around if you back off and let her work through things on her own time. She has to want this for herself; your job is to lie low.