My heart goes out to you. My second child, a girl, was much like your daughter. Unless you've had a child like this it is difficult to imagine how stressful and troublesome living it is. The lack of sleep in grueling. I have found that sleeping, eating and good behavior are all tied together (even for us adults). When one is off it throws the others out of wack.
I firmly believe if you don't mind having your child in your bed, then, why not? You both need your sleep. She sounds very tired, her behaviors are that of an exhausted child. The more tired some children are the more hyped up, active and unreasonable they become.
When my child would thrash around and kick during her tantrums I would wrap a blank or my arms around her and hold her firmly sitting in a chair or lying on the bed, if it were bedtime, until she calmed down (it may take away). Young toddlers cannot be reasoned with.
Although she may lash out and bully, it is not personal. She does not regard your feelings when she is acting out. She wants what she wants and is going to do what she thinks will get her that, even if she is wrong. She loves you but will still try anything to have her way. I have five beautiful smart loving children who seem unscrupulous at times in attempts to get what they want. It just gets more sophisticated with age.
If you are going into nutrition you know how important a healthy diet is. My daughter is very sensitive to food. Any caffine, milk, or sugar (including refined wheat products) have a direct effect on behavior. Keeping a food diary for her might help.
I did, and do a lot of reading to help me parent the best I can. I found "Raising you Spirited Child" very helpful. I saw someone recommended "The Happiest Toddler on the Block" and I'm going to go get it. My two year old is following closly in her sister's steps. But having gone through it once, it's easier the second time.
One a positive note, my daughter is now eight and we have a great relationship. She is turning out well even with her fiery temper and iron will. Take care and I hope the responses gives you some hope and answers you need.