My question is why does the kids machine need to be connect to the machine that connects to your network in the first place if it has it's own internet access? It seems to me that employee of yours must use the LAN to access the internet otherwise I see no purpose in connecting it to the LAN.

In my humble opinion, the risks are minimal since access to your company's network must be protected with a login and password for sure?!?! Unless your employee stores that login / password on his computer, even if his machine was compromised and a cracker took control of it, the cracker still wouldn't have access to your network. Off course, he would have access to the files your employee has downloaded to his HD though...

I think the best solution is to have that LAN disconnected since that machine is clearly supposed not to access the internet. The risk is minimal but still there...