Dear Tracy
I'm not going to tell you I have this down, because I don't! My son is now 13 and started with this arguing and talking back constantly since 11. I used Growing Kid God's Way, by Gary and Marie Ezzo, since he was 2. He is extremely strong willed and hasn't had a father really involved and has since died about 6 years ago.
Be assured, the blessing is your daughter is a leader and you need to channel this behavior to be her strength for her someday. Let her know how special she is, in this. Remind her, that she is part of the family and important but you are still the parent and are thus responsible for her safety and welfare.
My son also, does not back down. I have taken away the priviledges and added responsibilities. I also try to take the time in that day, maybe not just when all has happened {usually I don't have the time right then or maybe not level headed}. I explain to him, that I would like to bless him and can't now because of this behavior and start taking things away. Starting with dessert or computer, TV, friends. I've had him write out a chart, of attitudes and results of attitudes, which has seemed to work. I check off the good and bad. It's a visual, which he can't argue with.
We sit and talk also about choices and that he has control over what he chooses to think about, read, watch and involve himself in. This influences his actions and ultimately his enjoyment. Because if he is not doing as he should then it is guarenteed that he will regret by missing out on some great activity or treat!
These are just some of the things we've done in our family to help my son. After all, it's his character I'm concerned about. This will shape his whole future and is more important than what college or career that he has. I hope this helps a little. Ultimately, if she is wanting to control everything and be grown up, she will have to accept responsibility for her decisions, so start now with small things.
God bless,
D.