>>> It took me half an hour 2 weekends ago to get her change into her pajamas so I could wash her clothes.<<<

Eh, just don't wash the clothes. I would give her the consequence (whatever the situation is at the moment) after the first round of her arguing with me.

This is definitely an age related issue, my SD10 does the exact same thing. I got frustrated with her a few weeks ago and snapped at her, well SO said just let me know if you get frustrated, I'll deal with it, things are really delicate with her mom right now (so many BM issues right now!). And that's exactly what you should do, it's hard, boy do I know how hard it is. Especially if they are slow to "deal with it" or even worse if they don't "deal with it" at all! I'm really working on this one too, so my plan is "I'm not going to argue with you." and then physically walk away. Not my kid, not my problem. Now say it with me, "Not my kid, not my problem!"

Click here: http://www.steptogether.org/disengaging.html

We had this same issue. Until DH actually put his foot down, SD14 would continue to argue. He did the 3 strike rule. He'd ask her to do something and at the end of the request say "I don't want any arguments, just do it" and told her if she said one word, there would be a consequence.

Case in point; DH: "SD go empty the dishwasher please, no argument"
SD: "but daddddyyyyyyy, I'm texting X right now"
DH: "Strike One. I said no argument, you've just lost your phone for the evening - hand it over"
SD: "But dadddddddyyyyyy, I wanted to text her back and then I'd do what you said"
DH: "Strike Two. You just lost tv for the evening, care to keep going?"
SD: "You're so mean!"
DH: "Strike Three: Empty the dishwasher, take your shower NOW and go to bed"
SD: Gets up and goes to empty the dishwasher, which takes all of 3 minutes then showers and goes to bed, crying of course.

Next day:

DH: "SD, please take the trash downstairs"
SD: "Ok dad" and takes the trash downstairs, no argument, no nothing.

Of course, she'd still slip and try to argue her way out of something, but generally all DH would have to do is remind her of the 3 strikes and she'd stop.

Before I explained to DH that you shouldn't allow your child to backtalk or argue with their parent, it went like this:
DH: "SD please do me a favor and clean your room"
SD: "But dadddddy, I wanted to watch my show and then call mom"
DH: "Ok, do it after your show"
SD: "But dadddddy, I wanted to call mom after my show"
DH: "Fine, do it after you're done on the phone with your mom"
SD: "But daddddddy, it's not even dirty, so why do I need to clean it?"

And on and on it would go for a good 30 minutes. I was floored when I witnessed it for the first time and asked DH if he was allowed to argue with his parents when they asked him to do something. Of course, the answer was no. So, then I asked, "so why are you letting your kid argue with you? You're the parent here!"

I've tried the exact thing with SO several times, telling him that it shows his own daughter does not respect him and that it will only get worse with time. But in one ear and out the other. The arguing and backtalk drives her Grandparents and even her BM crazy, but with BM causing us so many problems right now, blaming everything on me and saying she doesn't even want SD10 around me, I just have to be done, so I just walk away.

Plain and Simple tell her:

I dont play games. this is OUR house not your mothers house. when you come here to do as we say. end of story.
You clean your room. You are polite and respectful.
Dont test me. If you want me to respect you. start respecting me.

...
DONT GIVE IN!!!!!!!!!!!!!!!!!!