Been there, done that. My eldest was a very anxious highly strung child who had tantrums/violent meltdowns all the time at that age.
OP, the good news is you don't have to control her. You need to take her out of harm's way obviously, you need to remove her so she doesn't inconvenience others or damage property, you need to make sure she doesn't get to hurt you.
But what you do not need to do is to suddenly and magically turn her into a lovely child who never tantrums. That is not your remit, so if you don't manage that you haven't failed.
If she screams and thrashes but you don't give her the sweets or whatever, then you haven't failed. She will learn eventually that screaming doesn't get her anywhere. But even so it may take some time before she has the impulse control to act on what she's learnt. That's not your failure.
I would start by thinking about what triggers can be avoided. Is she perhaps too young for ballet? (really doesn't matter if toddler ballet works brilliantly for other children, doesn't mean it has to work for her). If so, maybe think of cancelling.
Or is it more that the ballet as such is not a problem but that she sometimes tantrums when she gets overtired? If so, prepare yourself to carrying her outside bodily when she starts screaming. Take her straight home, or at least to a quiet place outside where she can calm down before you take her home.
If she hits you, either remove yourself, or if you can't hold her hands, firmly but gently, to stop her. It is reassuring for her to learn that she can't hurt anyone, that someone is stronger than her own overpowering emotions.
The calmer you can stay, the better.
The sleep question is a very individual thing. We decided we would all get a better quality of sleep if we just let dd stay in our bed if she came in at night. She was an anxious child, it reassured her and made her overall calmer. But if you find it is better to go the other way, you've had lots of good advice.
If she can't nap in the day is there some other way of giving her downtime. I used to lie on the sofa with dd and listen to music until she drifted off.