My thoughts Woven, fwiw.

It sounds like she could be protective of her relationship with her dad, maybe seeing you as a rival. Of course you are not. Her relationship with him is unique same as his relationship with you is unique. They can coexist easily. But I wonder if she maybe feels threatened when she has no need to but she may be coming from a place of insecurity. I may of course be wrong about this.

I don’t think it’s wise of him to pass on the info about what she said about you, that’s just my opinion and it’s not something I would’ve done personally. I’m not sure what he hopes to achieve by doing this, what his rationale is. Have you asked him? You don’t have to answer me btw.

I don’t personally feel making an extra effort would be the right thing here - maybe she might push back against this? Especially if she’s already feeling insecure. It sounds to me like you’ve already tried, it’s not your responsibility to try to get her to like you. I personally am a people pleaser so I would probably have to stop myself at this point, I don’t know if that’s relevant to you.

Is it possible you can ease back to just keeping socialising to the two of you for a while? To take the pressure off?

Hugs to you, it does sound like it’s been a little tricky.