Normally speaking for myself only, I attempted to separate the parties involved and then would interview the parties involved. If that does not work then, after careful consideration I make a decision on who to punish. Worked with all my children. Sometimes they (my children) even thanked me.
NTI: Your approach sounds very sensible. Wood: unfortunately your approach did not seem to do anything for the kids in my public school where every morning we said The Lord’s Prayer, read a student selected verse from Psalms, and pledged allegiance to the Flag. Oh, maybe the problem was that it was before “under God” was added to the Pledge. Nor did attendance at Catholic school do anything for the 3 bi^&*es in my Girl Scout Troop. In fact, maybe they were so fed up with being rulered by the nuns that they needed a smaller victim.