Try being proactive. While you are reasonably sure that your children will fight over that “toy” also believe that your children will work things out. “I see two children and one toy, and I know you two can work things out together so both of you are happy.” Believe it and walk out of the room. You’ll be surprised.
Allow bad feelings to be aired. How often have you said or heard “Oh I needed to say that and get it out of my system .Now I feel OK”. Understand that children need to do that as well. Tell them that if they are hurt they can express their feelings through words and not actions (you’ll need to control the kind of words used as well to ensure that they understand that abusing is not acceptable). Once the bad feelings are out, the good feelings will come back.