I’m afraid there isn’t much you can do about the relationship with the daughter. She is only 9. She is caught in a bind. She can’t like you because that makes her mother upset with her. She is dependent on her mom so she has to at least pretend to agree with her mother. Meanwhile, her mother can’t stand you because at one point her daughter loved you best. That may have been deserved but it doesn’t matter. She is insecure and immature. Rather than look at what needed to be changed in her own relationship with her daughter, she came up with stories that she hoped would eject you from the family.
Your fiance really has to stay civil with his ex. She is the mother of his child. If he makes too big of an issue with her, she is likely to separate him from his child. That would be terrible for the little girl. The most loving and kind thing you can do for her (and for your guy) is help her maintain contact with her dad. Please don’t hate that he sees her. It’s a big statement that he is a quality guy that he makes the effort to maintain the relationship. When she is older, she is likely to see for herself what went on. It often happens. At that point, she will be able to make a separate adult relationship with you.
There is nothing you can do about the women in your fiance’s family either. My guess is that his ex has let his mother know that she won’t see her grandchild if she accepts you. If so, that complicates things further. The only person who might be able to change their minds is your fiance. I hope he has made it clear that you are his choice and that you don’t deserve the treatment you got from your ex. He might be able to help them see his daughter regardless of his ex’s threats. But maybe not. If he’s done what he could, please let it go. Focus on the fact that your fiance loves you and is choosing you in spite of his family’s feelings about it. That’s huge. Make a good life with your guy. Find something meaningful to do on the evenings he’s with his daughter. And focus on how lucky the two of you are to have found each other.
I wish you well.