Dating a single father and need urgent help with his 13yr daughter. Help pls?

I love my boyfriend. We've been dating for a year now and things were great until about 4,5 months ago. His daughter is 13 and we got along so well first but she completely changed. She acts different around him and she's completely different when he's not around. Her mother is full of drama and she's given my boyfriend such a hard time when her daughter spends a good weekend or sth with us. Things got really bitter and I kept telling him that he's daughter is lying about me and she's changed a lot. She'd tell me she want to have more girly time with me, go shopping... and she'd go and tell him that I was ignoring her and she doesn't feel welcomed at his place because of me. I told him that may be someone is telling her things and that's probably why she changed.
Long story short,2 weeks ago we all went to the movies. I asked her how she's doing with school. she got upset and ignored us the entire time. He spoke to her that night and he was so surprised because she told him that her mother tells her I am trying to take him away from her (the daughter) and that I don't want his daughter... It didn't come as a surprise to me because I've felt and seen how his daughter changed and she lies a lot and gets so dramatic. Yesterday it was his birthday and at some point she started crying in the car and when we got to the destination, I had to leave them alone so he can talk to her and he even told her to stop being dramatic and upset "over the most ridiculous things". Again last night, we went to a Christmas lighting which she insisted on going and I had to drop my work and go so I don't bail on them last minute. We didn't even stay for 10min she said she wants to go b/c the "Christmas tree isn't as big as" she wanted. I said we still can make the best out of it since we're out there and just enjoy... and of course she got upset.
This is happening on a regular basis and my boyfriend keeps telling me that he's feeling like he's being stuck in the middle. I don't know how to deal with it anymore.
Dating a single father and need urgent help with his 13yr daughter. Help pls?
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