As I understand it, Skolelinux (like Edubuntu) is a client-server system that allows you to run terminals off of a main server in an educational environment. Not what you want here.
I don't really see what could be "targeted for kids", it isn't like the system would have a different UI. All that is different in Skolelinux is the bundled software, which you could install on any distribution.
Your best bet would be to simply install Xubuntu (which would be the best suited to the hardware, as I guess you have already figured out) and install the tools he would need to do his school work, and not much else. You can easily limit what software is installed, so you could for example put OpenOffice on there, but leave off Pidgin so he doesn't chat with his friends all night. Or put Firefox on, but make sure to configure everything to go through some kid-friendly proxy.