She already has a diagnosis for ADHD. I'm not saying this is correct or not; it's always worth keeping an open mind. But really - ADHD not well controlled CAN produce this level of anger in the child, especially if you have medication rebound adding to the problems.
If you can, try to get into her head, see the world through her eyes. I'm not saying here that really, she is being reasonable and you are not - of course I'm not saying that. But if you can, for a few minutes, switch off your "I am a reasonable human being and her mother" mode and put yourself in your daughter's head, you might get a better idea of what is going on.
A diagnosis of something like bipolar, should really only me bade if there can be no reason found for the intense mood swings. I remember the mood swings in y childhood and adolescence - I recall reasons for them, every time. Maybe not reasons that my mother thought sensible, but they made sense to me. Kids hurt for different reasons than we expect - difficult child 3 was pushed out of a tree by his best friend when he was 5 years old. He fell 2 metres and landed on his head in the rockery. He was concussed and crying. Why was he crying? Not because his best friend pushed him. Not because he was injured. But because he'd been eating an ice cream up the tree and had dropped it in the fall. He found the ice cream and began to eat it again. He immediately stopped crying. or difficult child 3 - this is normal.
I have seen both my boys go through anger such as you describe in your daughter. I remember difficult child 1 at the age of 6 - he could get very aggressive; he could also get very depressed and withdrawn. He was almost always bouncing off the walls and the more anxious he became, the more restless. His teacher at the time was insistent on kids sitting still and quietly; she scared him so he was even more restless and she was certain he was fidgetting on purpose, just to upset her. She sent notes home in his bag to organise a meeting with me, even though she knew he was badly disorganised. Then when I missed the meeting (because I never got the note) she made me wait another two weeks before she would say what the problem was. By the time the meeting was held she was almost incoherent and shaking. It was left to the school counsellor to tell me of the concerns. They had done a school IQ test on difficult child 1 (I didn't know I was supposed to be asked for permission first) which of course difficult child 1 failed to complete because he was too fidgettty; it was scored as if he had completed it and then the results analysed as if he had been trying to complete the whole test but been unable to for lack of ability. Bizarre - I was getting statements like, "Your son can do X in the classroom but the testing indicates X is actually beyond him. Therefore he can only do X because you have coached him..." all aimed to criticise my parenting not only of difficult child 1, but of easy child.
I was also being told by the school counsellor and this teacher, that difficult child 1 was seriously emotionally disturbed. I had seen this teacher in action with another "different" kid (with hindsight, I believe this other kid was Aspie - interestingly, he and difficult child 1 had gravitated together, but they left the area soon after).
What I'm saying - try to not diagnose her yourself, although having a range of possibilities in consideration is a good idea, I reckon.
Your daughter sounds very angry. Since the world is not working according to her rules, this is not surprising. She and you are clashing - this is probably also upsetting her but making her angry with you as well as with herself. At some level she is aware that she and her sisters are not as similar to each other as she feels they should be - she knows at some level that something doesn't fit and tihs makes her feel off balance which also could be making her feel angry. It's like the world has a big secret they're all keeping from her and she wants to lash out and make them be nice to her and include her.
When you're wired a bit differently, it's very easy to feel like an outsider. We react differently to this - some kids get withdrawn, some get angry, others get even. Some try to reach out more, some give up more easily. Some have often tried harder than we give them credit for so we shouldn't be critical of any kid who seems to have stopped trying. They're kids, after all - they've never had to do this before and they're learning as they go.
Try to get your hands on "The Explosive Child" by Ross Greene. It helps you find a way to mesh with your daughter that should be easier for you both, and at the same time help you understand her better. I found this book made things a lot easier for me. It's not a cure, but it definitely can help you feel more capable and confident. It's also OK to use the same methods for your other children (all kids can do well with these methods; it actually helps teach self-determination a lot sooner which is a good thing) so you don't have to worry about different standards (or double standards) in the house.
Having a physical outlet for anger is a good thing. Can-crushing is one suggestion - I don't see anything wrong with it. We bought a jogging trampoline for difficult child 1 and when he was bouncing off the walls I would send him to jump on the trampoline. Because it was small and low to the ground, it was OK to have inside. If we needed to, we could unscrew the legs off it and roll it behind a cupboard. Then difficult child 1 decided that going outside and sitting in the tree helped when he was upset. We hung a cargo net in the tree and both boys would climb into the net, they said it helped them feel better.
YOu can involve the child in some of these decisions too, but read the book first. Read around tis site, including the archives, because you are definitely not alone. Get your husband to come here too if you can, it will help him stay on track with everything you're trying to do.
I know you're trying to keep things as all one big family, but I do think at some point you are going to have to tell them the full story, it might explain some things inside your daughter that at the moment are confusing her.
Marg