Initially I felt that it was an overreaction to a non-event, but as someone else said earlier in the thread, 'how would you feel if this was the guy's spouse / brother / friend instead of his child ?' That's a good point.
Whilst I sympathise with the ATCO who is going to get the bullet, I have to say that he brought it on himself. You have to have rules, and rules have to be followed - moreso in safety critical areas like aviation. They can't do anything but come down hard on him. If the incident passed without repercussion, it's logical to assume it would be repeated - if not by this particular chap. Allowing anyone other than qualified ATCOs to issue instructions to aircrews cannot be tolerated - not because of the risk, or lack of, in individual scenarios, but because of the need for a clearly defined policy that everyone understands and no-one breaks.
I believe this chap isn't guilty of putting any flights at risk by allowing his kid on the RT, but he is guilty of being an idiot for thinking nobody would raise an eyebrow.