Start With Compassion
Remember that these are kids we are talking about. Kids will act out for attention, as symptoms of other problems, or simply because they don’t know any better. How many of us have had our kid say something completely embarrassing because they have no filter from thought to speech? So have compassion for the offending kid (and their potentially mortified parent).

Part of a compassionate approach is to show attention first to the child on the receiving end of the behavior. Check with them on how they feel and ask them what happened. You can’t control another person’s child anyway, so just focus on your own.