OK, lets take the hair as an example of what I'm talking about. She just doesn't care if her hair is brushed. Does she care if she leaves the house, EVER? The choice isn't to brush or not to brush, but brush and go out or don't brush and sit home. That's how it's modeled at school. Their choice isn't do work or don't do work, the choice is in how and where, but the work MUST get done, just like hair brushing MUST get done.
Giving kids a choice is giving kids control. You even stated that you don't force them to do their homework, so they happily do it for hours - not forced, their choice. The things that MUST get done in the home should be presented the same way, but that's where we as parents get stuck. How do we present it so that they think it's THEIR idea. Buy turning an "order" or "request" into an option they have to think about. You can clean your room and have a sleepover, or no sleep over. Eat your peas or not, but if you don't finish your dinner (peas are part of the dinner) then there is no dessert. The choice is there for THEM to make. Here's where it gets even trickier. Once you give them their options, you stop talking. Do not engage in subsequent 'why's or negotiations or explanations. If you MUST say something because they are going on and on, remind them of their choice. Just like at school, some problems will still crop up, but the number and intensity should diminish.
Hitting. What are the consequences in your home for hitting? Is there a consistent follow through? When everyone is calm, are the actions and the consequences discussed AGAIN. I view hitting the same as cursing. It's a lame tool of the uneducated mind. IOW when the brain gets so frazzled that it can't find the next thought or word for an argument, it reaches for these "tools of last resort". The second a person starts to cuss or hit, they automatically lost the argument, because they either don't have a valid argument or the brain is no longer functioning sufficiently to argue. Kids need to be taught to recognize this and stop and cool down.
See, I always thought my kids wold take my word as gospel. I thought the whole "parents are stooooooooooopid" thing only started when kids became teenagers. How wrong I was! My first time it REALLY struck me was when son just started pre-K (no dxes yet - I thought the kid was a genius). He came home and said, "Mom, your name is *Keeeeesta*" He mispronounced it. "No, my name is *KAYSTA*" (spelled phonetically to get the picture here) He refused to believe me and kept arguing, and since he saw me riled up started saying my name over and over the WRONG way. I found out they were teaching kids their 'vital statistics' and the teacher had told him my name incorrectly. I picked up the phone to talk to teacher, but she was already gone, and guess what? It was a 3 day weekend! I had to endure 3 1/2 more days of this! After the long weekend, I called the teacher first thing in the morning. She promised she'd correct him that day. Sure enough he came home that day and said "Hey, Mom, you were right! Your name is *KAYSTA*"
Point is, Mom was WRONG, teacher was RIGHT until proven otherwise. (and by the way having husband tell him he was wrong didn't help either) Many many times over the years, the kids just refused to believe me on things until they found their own 'proof'. And this includes things like brushing hair and teeth, taking baths, buckling in the car, etc. They need to get proof from the outside world (teachers, peers, TV, internet) that what Mom is asking for, falls within the scope of "normal" human expectations. I don't know why. I finally got to a place where I don't care why. I just find ways to get them their "proof" All three are currently in therapy just to give them "proof" that what mom is telling them things that are true and right.