Will, it can always be tricky receiving grief from the sidlelines. Personally I will use almost a stepped approach, in this I mean first making them aware from about 15 yards away that you don't want to hear anymore from them, next I would go over, isolate the coach in question and tell him in no uncertain terms that if you have to come over again it will be to ask him to leave the technical area.
They think they can get away with anything if they are classed as the "physio" but one way around this is to ask the opposing team. "If a player goes down injured, would you mind dealing with the injury on the other clubs behalf?"
The threat is usually enough to calm him down though and if he knows he is the only one he would be daft not to clam down, the only time I have gone beyond just having a word is when i did the above only for him to come back with, "send me off then, do I look like I give a f***", Goodbye fella!!