Terrific response from Krista re: how you can respond to your daughter to show her that her choices are not good ones.
I would add, be calm and very quick: When she grabs something on a play date and dramatically yells she won't give it back (for example), give her one warning, be very clear that it's her one and only warning --her chance to give the toy back -- and when she won't, leave! Swifly, no discussion, you're out the door. It's tough on play dates but if you tell the other parent that this will be the reaction immediately upon her acting a certain way, the parent will understand and help you out, I'm sure. I've seen it work in our old playgroup.
Say to your daughter, "You had your one warning and you're choosing not to play nicely, so we have to leave now. Goodbye (other mom). I'm sorry but we can't stay because Sally can't play with others well today." Then leave. If Sally decides, seeing she's about to be hauled off, that "Mommy, I'll give it back! I'll be good!" that doesn't matter - don't back down or cave in then, even if she's yelling that she'll be good; the deed is done, and you just have to smile sadly and say, "Sorry honey, you had the warning, you didn't listen and give back the toy when asked, and we still have to leave." A few times of very swift, non-negotiable departures from play dates, birthday parties, the park, and any other fun situation may show her that she will miss the fun if she goes for the drama. I hope it works for her strong-willed self; I have seen it work for other kids. It's hard on the parent, though, especially if she's wailing in the car afterward and pouting the rest of the day.
Is she in first grade if she's six? How does she manage at school? Are the girls she has trouble compromising with girls she sees there, or girls who have been longtime friends outside school? If she's in first or K, talk to her teacher about her social skills during the school day. The teacher may observe things that will surprise you, like finding your daughter compromises more with other kids at school than you see her compromising with her friends outside school. If not-- well, the teacher and you could work together on building her skill at playing more cooperatively.