For the job you want to do XP pro is your best bet, and then you could set group policy to how you want it. But since I presume you are working with XP Home, am I right? There may be an alternative...
But I am sure in XP home, you can select Run As...
When you right click on the program. This would allow you to then run JUST THAT PROGRAM in Admin account, you should then be able to set this so this program always runs in admin.
Instructions for this are:
Make sure it is the main link, not a shortcut to the game, maybe one from the start menu.
Then right click on the main link to the game, then select Run As...
A dialog box appears, click the bolb next to Run as the following user:
Then put in your username, or select it from the drop down, then type your password in the box below that, then click ok, the program should run with NO problems.
However you may have to do this every time your kids run the game, I am not sure, give it a try and see what happens.
It is good your children cannot run software themselves from my point of view, it stops them installing or removing things that need to be there, such as your Antivirus or Firewall app.
Anyway, hope I was of help.
PS. Let me know if you need more help.