Hi again
A little bit more on the 'behaviour modification' we went through with DS, although he may have been a bit younger than your DD when we started.
We were advised to find an instant gratification treat (in our case it was a jellybean) and every time we saw him being good we gave him a treat with "well done, good behaviour" or something similar. This was very tedious in the first few days/weeks as you had to be very consistent and
very frequent with it. With less and less as the weeks went by as his behaviour improved. On the flip side everytime he went into a paddy we had to walk away from him (I used to walk round the house) so he got the message load and clear good behaviour got a treat and tantrums resulted in loss of attention. As he got older the jellybeans morphed into coins which went in to his money box, and we still reward very good behaviour with coins if appropriate but he really doesn't need it now as his behaviour is pretty much amazing now.
The other thing we used to do when he was mis-behaving badly and it wasn't a walk-away-from tantrum was to send him to his room and tell him he could come back and join us: i. when he was ready to calm down and behave properly and ii. when he was ready to apologise for his mis-demeanors. To begin with it was a struggle to get him to stay in his room and calm down but we stuck with it, I swear its harder on the parent than the kids.
DH still does a lot of positive praise and rewards for good efforts and behaviour which I tend to think could be eased back on now as I'd like to think he behaves well because he wants to and not just for the rewards. But maybe the balance between us works because as I said he really is a great kid now, with great manners but if you'd asked me if I'd feel this way a few years ago I'd have said you must be joking, I saw me or him or both of us in straight jackets and a padded room.
Good luck - I do know how it feels and I'm so glad I got the advise I did when I did and that we were both determined to see it through (we were willing to go with it because we were at our wits end) and now I have a wee charmer who brings us great joy (his teacher aide keeps threatening to steal him, she loves him to bits).