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If they pushed and shoved they're should have been technicals.... Thats a fight. Anytime someone says there could have been or should have been a tech. i stop listening becasue you should have taken care of business. You cant demand that a player be removed. Something that coaches appreciate is when you tell them that a player is in trouble. I had a kid snap back at me one night on a call I made. I nodded my head to acknowlege him and jogged off to report the foul. I came back down to his coach and said
"Might wanna check on 33 coach, he's gunna get in trouble if he keeps it up". coach didnt ask a word said thanks man and turned to his bench. After the first free throw well I'll be sub at the table and 33 is jogging off the court asking what he did. Coach chewed his but for running his mouth. Ask Hawks Coach, he probably really appreciates it when referees tell him his players are at the end of their rope and might get a technical.

Now in your situation you either have a pair of T's or you ignore A's coach.

I had a situation friday night. Two players started talking trash to each other on the post play. I looked to see where the ball was and popped my whistle walked up between them and very politly told them that if they kept it up both of them would get a technical foul and likely be on the bench. I said it quiet enough for both to hear. Both coaches recognized the situation and hollard out to me they want to sub em. I dont think either player ever came back into the game.

Its all about the situation. You cant tell a coach to sub a player out but you can strongly suggest before a player gets a T. But if your situation happened as you described they're should have been a T on each player. Not necessarily ejecttion for fighting. However you could justify it as one if it would make the game better.