The sleep thing makes me really suspect some other problems, like sensory or auditory (Auditory Processing Disorders (APD)) problems. I would work hard to get a PRIVATE Occupational Therapist (OT) evaluation for sensory issues and a complet Speech Language Pathologist (SLP) evaluation. Yes, school CAN do Occupational Therapist (OT) evaluations, but they ONLY look for how it causes school problems. Private evaluations look for how it causes problems in her entire life. It may seem strange that a tag or a seam in yoru sock could be such a big deal as to overwhelm you, but it really can be that bad. I have significant sensory issues, now made far worse by nerve problems (not nervous, the actual nerves are all messed up and no one can figure out how to help - totally annoying). If I have a shirt that itches, I literally CANNOT focus on ANYTHING. I never could. Thank God that my mother had to wear itchy clothes as a kid and swore that her kids would NEVER have to wear things that itched. She held to that and even made all of my clothes until I was about 11, even my school uniforms. She even made me a promise when I was 10 that my wedding dress would be as comfy as my jeans. It was - and I was pregnant and cranky as all get out! It was exactly what I wanted (NOT white, lol, pink and green with tulips all over) and the skirt came off and there were shorts to wear at the reception. I probably would not have worn a dress if she hadn't made that outfit.
It is entirely possible that just attending school could stress your daughter enough that she is fried when she gets home. Until 3rd gr my youngest missed at LEAST 1/4 of the school year with absences written off by his 504 plan because he would get so overwhelmed with sensory things that he would just sit and shake and shake and shake from the stress and overload. If I sent him to school like that he just shut down, would go where he was told but couldn't talk or function really. Then t would take 4-5 days of no school to get him back to normal. We also kept certain foods out of his diet - tomato, dairy, orange, pineapple, and artif sweeteners until he was 5 and then we only added small amts of dairy and tomato. mostly pizza for tomato and cheese for dairy. He doesn't like milk unless it is cooked because it makes hm feel yucky. We listened to that even before we learned about his food allerges and never pushed it. He LIKES soy milk and we keep that for him. It makes a big difference even though the tomato and dairy were not really "allergies" or even sensitivities that the allergy doctor could find. WE saw it changed his skin and what he could cope with, so we did what seemed right for him.
How much protein does she eat? Some kids just need more than others. I keep those protein bars around, the balance and zone brands have 40% carb, 30% protein and 30% fat and are the best balanced for healthy diets, and giving them instead of candy, esp when we have an afterschool activity, makes a HUGE difference. We also keep jerky, lean meats, cheese sticks, etc... on hand and encourage the kids to eat those before they go to snack foods. If we go ANYWHERE after school the kids get a protein bar or protein snack. If we have to go to Walmart and I don't remember a snack, we get popcorn chicken from the deli. It makes a HUGE difference to my kids.
Changing parenting is important. Have you read The Explosive Child by ROss Greene and What Your Explosive Child is Trying to Tell You by Doug Riley? They are CRUCIAL. The hitting has to be Basket A, or the top priority. You only work on 1-2 basket A things (non-negotiable), then the rest are basket B (medication priority) or basket C (low priority or ignore it at least for now level). The Explosive Child explains this very well. It IS different parenting from teh normal, but our kids don't think the way easy child's do so this works for them.
It is just as important for you to not cuddle difficult child after she hits you as it is for her to nto have to hug anyone she doesn't want to. Making a child hug someone when they don't want to teaches them that their instincts are not important and they don't ahve the right to say taht someone can't touch them. Making you cuddle her after she hurts you teaches her that she can hurt others and they have no right to say that she can't touch them any way she wants whenever seh wants. Basically it is a way to teach her taht she can hurt people and they still have to accept her hugs even if they are still in pain. Neither one is a good or safe message for her to learn. It may seem harsh to put it this way, but it can help you make her watn to learn to stop hitting. It won't owrk that way at first, but seh still has to learn the lessons.
A parent report is an excellent thing, in my opinion the most powerful tool in the Warrior Mom arsenal second to your instincts. That is why it is in my sig, that and I keep forgetting where to find it when I want to tell people about it.
I am glad your husband is supportive and I understand the catch-22. I am glad I was wrong and he is supportive.
PLEASE get an appointment with the domestic violence center to get their help to teach her to stop being abusive and to help YOU with the feelings that being chronically abused creates - because no matter how much you love you daughter, she is still abusing you and you still need to deal with that.