CVA, I haven't had a chance yet to read back very far, but I thought I could add something that might be off use. Nearly all girls like to do something special, something 'just theirs'.
Whereas I bet your boys would be happy throwing around a ball at the local highschool or playing a racing video game with you - your daughter will likely be over the moon if you plan or set up something special for her.
It doesn't have to be elaborate, just well thought out so that you're not asking "what would you like to do". Kind of like you're taking her on a date. She may react awkwardly at first, especially if she's not very outwardly emotional (in a positive way, nearly all 11-20 year old girls our outwardly emotional - speaking from experience heh)but she'll treasure these special Daddy/Daughter times. Take her to dinner, go to get icecream, buy her a new purse or earrings from Claire's, ask her questions like you would to someone on a first or second date, plan to redecorate her room with her (my friends and I moved our furniture and teen beat pictures around on a nearly weekly basis).
I'm sorry that you're going through this I hope the babysteps you're seeing keep on coming!
Me: 28 H: 29 Married 5 yrs Two sweet and ornery little ones 4 and 2.5