My two cents ... if your daughter sees you doing whatever you can to have more time with her, that will prove your sincerity. Be honest with her, but don't tell her things she can't yet understand. Always keep your word. Be her father first, her dad second, and her friend third. I just finished reading this novel where a teenage boy's father just for a moment decided to be "cool dad/friend" so his son would be happy with him, rather than be "responsible father", and it all went tragically wrong. It DID have a happy ending, though, and I love happy endings! Well, a bittersweet ending, actually.
I've raised 2 teenagers and made plenty of mistakes. I think professional counselling early on would have helped us understand each other and helped in communication. Nip problems in the bud sort of thing, rather than trying it later in the teen years when patterns are already firmly established and much damage has already been done.
And lots of "I love you's" and hugs! As I said, my two cents ..... LNO