I'm not quite sure what you're saying. "Stick a fork in it", is shortened from "stick a fork in me, I'm done", kind of a slang way for saying I'm out of here. Refers to food being "done".
I think sometimes, kids have humiliating experiences and it makes them stronger. The more appropriate response, IMHO, for the mother would be to tell her child well, sweetie, you were a great turkey and you did have two turns at the microphone. Did you notice the other kids only had one? So really, you got something extra.
When we treat our children like delicate little cupcakes and try to avenge every slight they might experience, we sell them way, way short, IMHO. I'm not quite sure why he was allowed to continue to go back on stage, but I think it was probably because the teachers didn't want to embarrass him by going up there and retrieving him. And then, thankfully that whole awful production was over and it was time to shut it down.
I don't know who wrote that "play". Maybe it's one they do every year - and I can see that it would have some educational value. But holy cow what a boring, long drawn out production that no one could understand and the natives were clearly becoming restless.
If that line he was about to ad lib was his only line in the production, and he was purposely denied that, I would feel absolutely completely differently and would feel he was truly wronged. As it is, some kids are kind of stage hogs and you can't always accommodate that.