I agree woith VictoriaChildCare. I have the same policy about fighting regarding a certain toy. I use a minute minder or maybe the other child can find something to trade for the popular toy.
I use time outs in our talking chair. When there is a problem the child or children sit in the talking chair and we discuss what has happened and how we can keep it from happening next time. I have learned that the time I spend talking to the child calms everyone down and then we can carry on playing. Conflict resolution is one of the best outcomes for children in a child care setting. They learn how to avoid the conflict and how to come to an understanding with their peers.
Hang in there and stick to your policy about fighting, hitting, punching, etc. There will be days that seem worse than others,but it will get better.