I think that it's a tough time for Dads when their DDs reach this stage, they feel like they are losing them and rightly so - I think it's needed for girl's to push their Dad away a bit.
What is important is that he doesn't push you away, and also that he handles it like any other dad in a "normal" together home.
If he doesn't, he will make you feel alienated and will create a Disney relationship between himself and his dd which believe me YOU DO NOT WANT. (Did I say that loud enough? 
How long have you been together? Is this a new thing relating to the stage she is reaching, or dos he have "disney" tendencies? Does he have guilt around the split? Do you get the impression that Mum is belittling him to your DSD or making a mockery of the time they spend together?
I would get him in a good mood and tell him you've noticed how hard it is for him with his DD reaching the stage where she isn't Daddy's little girl anymore. Do you have some anecdotes about your own experiences with your Dad at that time? Share these and let him know it's normal.
Tell him you want to support him through it and ask him not to block you out because it makes you feel the way his DD makes him feel.
Then plan some low key, low cost but interesting things to do as a four. They have to not be anything unnatural or over the top or allow dsd to feel she is being bought because that is a slippery slope! But I would say 50/50 time just chilling out at home (where he leaves her to her own devices and gives her space) and time doing things together.
We fell in to a bit of a pattern of DH doing something with his DD, and me doing something with mine. When his DD started to reject him, he started to resent my relationship with my DD as he didn't feel a part of it. He admitted to feeling jealous when he saw how close we were and didn't feel inclined to join in with things we did. Thus, he pushed himself further away and became more alienated. Both of his key relationships were breaking down and he was alone. Added to this, DSD's mum was playing every alienation trick in the book as DSd drifted further and further away until ultimately she disappeared for six months after a big unnecessary row between the two of them. It was a minor disagreement really but the excuse she'd been looking for to detach completely.
DH became so desperate that he compensated by dreaming up all these exclusive (and expensive) Daddy-Daughter dates in an attempt to "win her over" and make their time together enjoyable again and it was just horrendous. I ended up feeling like the OW, and that he was having an affair! And DSD just became more and more entitled to having daddy all to herself at the expense of all his other relationships. Then she'd drop him the minute she felt like it and he became dreadfully depressed. And I wasn't prepared to just be picked up when he had nothing better to do so I started living my own life too. It was a horrible time but we have had counselling and we all handle everything much better now. He doesn't block me out any more and if he has an episode where DSD is being awful, he will come to me and we'll either laugh or cry together about it. The counsellor pointed out to him that whilst we have a duty to put our children first when they need us. Those children soon fly the nest and they don't look back, so we have to put our partners top of the tree. What I had to do was show him he could trust me to put him first too, which means that sometimes I have to forgo time together if DSD turns up after an argument with her Mum and needs a hug, or if she wants to come to the cinema with us etc. What changed after the counselling is that he started to ask if I minded, and gives my feelings equal weight to his DD.
Had that not changed, we would definitely not be together. And DSD would be... well lord knows what a horrible brat she would have become if all that pandering and princessing had continued!
Sorry, that was a bit of an essay. But if I'd have known then, what I know now, I could have saved a lot of heartache.