I thought I should make a post about how we have been handling the fighting at our house. I was SO thankful for all the comments here on the blog and also on FB.
First, we have started role playing. Anytime the kids get upset at each other, I stop them and we calm down and act out again how everything should have happened. It is usually because a sibling or friend has taken a toy. So I make the offended calming ask nicely for the toy back, and the offender to give it back nicely (not throwing it at them) and say they are sorry. So far it is has worked well!
Funny story: I overheard a fight upstairs. Hannah had taken Andrew's beloved kitty cat off his bed. He was screaming for it. She calmly said, "Andrew, you must ask for it back nicely." He did and she gave it back. They are learning, now I just need to teach Hannah not to tease and take the toys in the first place!