we're I guess in a similar situation, I have remarried and DD lives with us. She is a bit older than your DD, 15 now, but we have been living with DH for just over 5 years now.
To start off with DH wouldn't really discipline or get to envolved with things like telling DD to do things, but this just didn't work, I think she saw him as a weak link, so he started taking charge, telling her to do her homework, or get ready for bed etc and things are working really well.
At times I think he overreacts to certain things, which I just don't think are that bad, but I just have a talk to him and to DD and things sort themselves out, but this doesn't happen very often any more.
I think that to be respected as a parent, you have to act like one, and show that you are the responsible adult, throwing a hissy fit and slamming doors wont do that iykwim.