You are her father. Your daughter is suffering in some way. If she rejects you or things you give her that doesn't mean you give up. At some point she will want you back in her life. What is she going to remeber: dad constantly being there or dad giving up on me? I can only imagine how difficult this is for you. But you're the parent. It's not up to your children to make you feel better. Parenting isn't all about the joys. It's tough work. And to balance things with your other children while not seeming to favor your oldest... I don't envy your situation.

But don't quit trying. It might take weeks, months, years. But she only has one father and you're lucky it's you Just keep loving her even if from afar. That is what I would want from my dad now and when I was a teen.