@Minttea77
You need to get the night sleeping sorted asap.
This is of the utmost importance. If you think it's beyond you and your husband's capability, please consider hiring a toddler sleep specialist. It will be money very well spent.
If you don't do this already, it might be a good idea to establish a fairly predictable daily routine.
Start with the two of you getting chores done. She can 'help' and you can tell her what a helpful big girl she is.
Try to get out from mid morning to just before lunch, rain or shine, so she can run and wear herself out.
Instead of napping during the day, try a nice warm bath after lunch (around 1 pm) followed by a spell wrapped up in blankets on the couch for both of you. She may well drift off to sleep there, or you could have storytime, listen to music, sing together, etc.
Then let her 'help' getting dinner together or give her something to 'clean' with baby wipes.
Do you have any space where she could do some sensory play - some ideas:
www.learning4kids.net/play-categories/list-of-sensory-play-ideas/
Children of two love to just feel different textures - running their hands through big basins of lentils or rice, or squeezing shaving foam+sand or water balloons not filled too full and tied off. This sort of activity is best undertaken in a small, confined space.
Sorting coloured pompoms with little plastic tweezers is fun too.
Do you have anywhere in your home or garden where she could bounce? You could use a mattress indoors.
Do you have a garden where you could put a sand pit?
All toddlers are doing the very best they can, and they have limited self control, though they are very teachable if you try to be consistent, kind and firm.
By the same token, you as a mother are doing the best you can too. Cut yourself some slack and forgive yourself for shouting.
It does no harm at all for your toddler to realise that you have your limits. In fact, it is really, really important for her to sort out in her head that you and she are separate people, that you have your own feelings, and that there are things she can't do because they upset you.
At this age, it is really, really important for her to sense the limits of acceptable behaviour on her part and to gain a glimmer of understanding of what is important to you, what behaviour you do not want and what behaviour you do want. Don't pussy foot around here for fear of hurting her feelings. She can learn what you expect only from your reaction to her behaviour. The odd shouty incident isn't a problem - it can actually serve as a way of teaching her what you expect from her as long as it's not your habitual way of communicating with her and as long as your expectations are age appropriate.
Tantrums are very trying. Sitting them out and then reconnecting with a hug if possible is the best way to deal with them. Don't worry about tantrums in public. Most people have been there and understand. You don't need to be concerned about the opinions of those who haven't or don't.
Your decision to take her out of the dance class was the right one. The teacher sounds very inexperienced. Strictness has no place in a toddler movement class.
Would you be able to find an online movement class DD could participate in along with you? She could prance around your sitting room.