When I have issues like this at my work I will(note this doesn't happen often) ask each child if they have something they would like to tell the other child and try to mediate a solution because like the fights normally start because kids feel they can't express their words on what is happening and maybe this will model how to avoid the fight next time.(before the mediation i ask each child to take a deep breath but it depends on the ages of the children involved)
But I am a teacher in a one day a week care center not a parent.
Hope this helps.