Sounds like my DS7, except he's not recovering from any serious injury. (I hope your DD is better soon.) But I am feeling pretty lucky that my DS's GT school does not give very much homework - just 30 minutes a day reading (which he does on the ride home, and no requirement that he read aloud, which I'm sure would stress him out), studying for spelling, plus on rare occasions he has to finish homework he didn't complete in class.
Even without much homework, he is a perfect angel at school and lately a real beast at home. He recently got all 4s (highest grade) on his report card for all things related to classroom behavior. I told him he should spread the love and get a few 2s in school so he doesn't save all the bad behavior for us at home.
When it got out of hand recently, we started shaving 15 minutes off his bedtime as a consequence. The extra sleep did seem to help (or maybe the threat of losing more time in the future).
Like others have said, I'd talk with the teacher to see how long she expects 7yos to be doing homework.
