Is my thinking wrong?
No, your thinking is appropriate.
Should I have simply ignored the coach the first time?
Definitely ignore the AC, I would even turn and address the HC, I don't need to hear from his bench, or issue a bench warning for the AC.
How can I say things better so the coach does not think that I have agreed to give him a call?
Don't address the AC; telling the HC, when he states, I hear you and thank him. Be nice and when it is time to take out the trash, be nice!
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