Hello there and welcome to the forums.
I've done quite a bit of research into thin clients but I've yet to find any that are suitable for gaming so I can't give you any recommendations to suit your needs I'm afraid. My kids (and indeed friends and neighbours too) also regularly "enhance" their computers and call upon me to sort them out. Only once did a problem require a total rebuild the rest were solved using a variety of tools (eg. Hijackthis, Spybot search and destroy). Obviously having decent anti-virus software helps too.
What I've now done with my youngest is I've set her up on her machine as a non-admin user and if she wants any new stuff installed I log on as me (an administrator) and I install it for her. This has decreased the amount of times she inadvertently "breaks" the machine. My eldest is an administrator on his machine tho since he is forever installing the latest "must have" piece of junk so I still regularly have to sort his machine out
But I'm confused by what you seem to have read. If you were to move your kids onto a thin client setup you'd simply be moving the problem from the desktop machine to the server, wouldn't you? Or am I missing something?