OP, this sounds very, very familiar to me...you sound like my now-DH and his DD, when we met! She was a bit older than your DD, that's all.
I really do encourage you to look for resources and help around the idea of 'spousification' especially. My DH had not exactly 'replaced' his first wife with DD (it is quite common for spousified children to take on adult responsibilities or act more mature than their years - this was not the case with my DSD - it was more than she was given adult privileges and encouraged to see herself as a peer, but without any responsibilities)...but he had very much allowed her to play at being his partner and allowed or even accidentally encouraged her to be quite domineering and pushy with others.
I found (and yes, still find, five years on!) my DH's parenting of DSD to be the biggest single obstacle to our relationship. It's affected the whole family dynamic and the lives of the other children. I should add that she's smart, engaging, creative, generous and I care for her very much.
The thing that my DH eventually realised, with a counselor's help, was that the situation wasn't very healthy for DSD herself. Since he's been working at redrawing boundaries and helping DSD back to a more appropriate role - that of his teenage child - she has become happier, easier to be around, has stronger friendships with others, and is finally catching up to her age-group.
We got some help from Relate. Parenting classes sound like a good idea too, but I think you would get a lot from a counselor who understood/had experience with the problem of spousified children.
I also recommend the book Stepcouplng by Susan Wisdom, it has a lot of good advice for creating a 'unified front' and putting your relationship as the two adults at the heart of a healthy family unit.