OK, I'll apologize for my tone.
I read your response as issuing the coach an ultimatum, even though the coach may or may not have even understood what you were talking about. Generally, prior to getting to the point you got to, threatening to eject him from the game, there are warnings put in place. I read nothing of any warnings, only you going to the coach and threatening to eject him.
I'm also not so sure a coach is responsible for the fans behavior either, I could be wrong. By rule, a head coach is responsible for the conduct of his players a