Wow, I am impressed at how mature your dd is!
How old is she?
I know how if feels not to share parenting ideals, because my dh also does not buy GD. In our case, and differently to yours, things are not going so well and that gives him even more ammunition. I have to say he has made truly incredible progress at handling the girls in a calm and composed manner, especially if I am not there, in the last few years, but nevertheless we still bicker about the girls' upbringing on a daily basis almost.
Through all this I have learnt that:
1) the no punishment ideal is truly a revolutionary concept, our whole society is built around the idea of rewards and punishments. So, it is not strange that your dh is afraid of embracing such a big change. He may feel like he does not have the skill to parent this way and therefore rejects the idea altogether.
2) so it is important for him to see that he has good skills as a parent, that he does not feel like he is not "as good as you" if you see what I mean.
3) the one big thing for us has been for me to learn to trust him to care for them on his own, and just go out and do my thing, so long that he promised he would not spank them ever. He knows that if he did that, they would tell me and I would change the lock the next day. It is my line in the sand. Their relationship has deepened, it is a different relationship from the one I have with the kids, but it is I think good in the end for them to see that there are different ways of doing things. He is a very caring dad, makes them good and healthy food, takes them to outings, also roughhouses them reads to them and plays cards and stuff. He did much less of all of this when I was more controlling of their relationship.
I hope this helps some.