Definitely wrong way to handle it.
The minute that starts, send the players back to the bench.
Call the head coaches to the middle of the field.
Make it very clear how you are going to call the game. Tell them the players will come back out and shake hands. if they do not do that, then they will be ejected before the game even starts. No lecture, no anger, just the facts.
At the first sign of trouble, make the call. If both sides are guilty of blatant penalties, etc., and it gets out of hand after that, go to each coach and threaten to call the game.
Somehow "shut up" just is not going to work. As an official I would also want to know who the AD is and where he is. If I suspected this was going to happen, then I'd find them and tell them the same thing. If the thing had been going on the whole first half, I would have found a way at halftime to call it off.
+1