In particular any PC used by a child is likely to have a useful life measured in months if not weeks
For anyone who hasn't already seen it several times, my solution to this one was as follows.
The first time a child got a nasty I pulled their network connection until such time as I had time to clean up their PC. So, no internet for a week. I explained that each time this happened it would take me twice as long to get round to dealing with it. Some child downloaded and installed and ran a virus a second time. Two weeks with no internet.
That was sufficient to get them to believe me. That was several years ago now. There have been no problems since - none of them wants to live without the internet for a month.