Another thing I've found that works really well to increase positive behaviour & decrease the negative stuff is to be quick with positive and negative reinforcement. Eg - she leaves kinda without a fuss, say right away, 'I think we'll go to KFC because I'm so happy that you were a good girl and didn't cry about going home today'. Or another example with my son: he tried to bring play doh into the loungerrom when he knows it's a kitchen toy 'right, I'm packing the play-doh away because you brought it into the loungeroom.' Then 2 mins later I asked if he wanted to play with the play-doh in the kitchen. When he brought it back into the loungeroom, I repeated the same process (and maybe a third time? can't remember). When he finally started to play with it in the kitchen & didn't bring it into the loungeroom, I gave him a square of chocolate & told him how happy I am that he's being a good boy & playing with the play-doh in the kitchen. Doing these small but immediate responses to his behaviour seems to help him learn the appropriate behavioiur pretty quickly & stamp out the negative stuff.

Maybe next time she asks for something you can say 'ok, because you did X (no matter how small initially) and I'm very happy with you for that', or 'no, because you did X and girls who do X don't get Y'. But try to do the former more so than the latter.. you want her to catch on that she gets what she wants when she behaves well, and she won't figure that out until she actually does get things she wants by behaving well. Once she starts to understand the way it works you can bring in the 'no, because you did X and girls who do X don't get Y' in response to negative behaviour. I think it's always good to try to keep it positive, even when responding to the negative behaviour. So when I say no, at the end I'll say something like, 'but we're going shopping this afternoon, so if you're good when we go shopping, then you can have <whatever has been requested>. Then before we arrive at the shops i'll reinforce it: 'remember you didn't get to do X because you did Y this morning?' (wait for acknowledgement), 'ok, but we're going shopping now and if you're a good boy and stay with me without running away while we shop, then afterwards we can do X. How does that sound?'

Sorry.. another long & rambling post. I hope something in there is useful. Keep us posted.