If she has anger management problems and the school are aware of this, coupled with the fact that she has clearly been trying harder to behave and the 'reward' thing worked before, I think it is dreadful that the teacher shouted so much at her! What sort of example does that set?? It earns the teacher absolutely no respect from the student and spectacularly backfires most of the time with kids like this.
My ds was getting into trouble quite a bit last year (yr 9) and things took a very negative turn. You know….seen as the bad kid and balled at a lot etc. The head shouted at him so much after ds had written sweary stuff on a friends planner that he was self harming by scratching his arm with his fingernail, underneath his shirt sleeve
during the telling off. The head didn't notice. He still has a scar to this day.
Since then, we have made the school aware of everything we are doing for him at home (psychotherapy), rewards and also the triggers to his self harm etc and the school have been brilliant in accepting that for him, to get good behaviour, he actually needs positivity. The HOY emailed all his teachers and asked them to be as positive as they could be with him and also with me and his dad at parents evening! 
This helped ds so much and I really appreciate how much effort his school have gone to, to help him. They seem to be seeing who he really is and trying their best for him.
In your dd's case this does not sound at all like this is happening and that is a shame and especially hard for you, I imagine, if you have seen lots of improvement with her behaviour at home.
I also agree that she shouldn't be punished at home for stuff she has been punished in school for.