To me, as a complete objective outsider, you have summed it up as 'unfortunate reputation' at home as a tantrum child. As children (and adults?) we so often live up to our reputations I think and then can't see a way out. Its easier to just carry on. I teach excluded kids and find that often a blind, denial, 'you are a fabulous child' approach can work, eg 'oh, you're helping me clear up, brilliant' - when they are clearly about to throw something across the room (much older kids of course - and I get to send them home at the end of the day).
Its hard for you because you are in the thick of it and don't have breathing space to think, reflect etc. So I think its quite impressive that you can identify this.
A counsellor will be able to talk to her and try and change those 'I am the tantrummy one that makes mummy sad' pathways, and if you can maintain a 'of course you are my lovely child', happy, postive atmosphere day-to-day approach (ha easier said than done,eh?) then hopefully you can have her back.
Its great she can be well-behaved and good natured at school but sometimes kids are grumpier at home because it is safe so please don't feel bad that she saves it all up for you!
Hope this makes sense and helps, it soudns like you have had loads of advice already...