I agree wholeheartedly with Gemini, but would add one more thing. I would NOT talk to her about these things again. That's putting adult responsibilities on a child. She doesn't have the capability yet to understand what is going on and why. It's bad enough that BM has put her in a position of feeling responsible for her mother's feelings. And all the more reason why counseling would be a good idea....regardless of what BM thinks about it. So what if BM takes you to court over it.........if you know it's the right thing to do and it's beneficial for your daughter, that's all that counts.
All your focus should be on is your daughter's well being. Keep going to her events........after what she's already told you, she NEEDS you to be there, even if she can't really tell you that. See, that is what the BM is counting on....that by constantly reinforcing to DD that you abandoned them, she will jump on every opportunity to verify that to her. Show up and keep being there, no matter how uncomfortable anyone makes it for you. Your presence will eventually tell your DD that you did NOT abandon her, regardless of what BM tells her.
But once you do get to court, make sure you include that DD canNOT call anyone else Mom or Dad except bio-parents. We had that happen too, in a way. We got married when SS was barely 4 y.o. and BM married exactly 2 weeks later. SS always came to up on DH's weekends with 2 bags, one with clothes and one with toys. A few months after BM got married, I happened to notice SS's toy bag had his first name and SF's last name on it. I showed it to DH and while DH took SS back, he asked SS what his name was. SS gave his first name, but SF's last name. Apparently after BM got married, SS either realized that her last name changed and assumed his did too (and BM refused to correct him), or she told him that it had. EIther way, it was wrong. DH told SS that his last name was still DH's and SS started to cry. So DH straightened it out with BM immediately and threatened her with legal action if she didn't cease and desist. We never had the problem again. And when all this came out, it appeared that BM and SF were also prompting SS to call SF dad, too.