This question already has an answer here:
Is there any program that is similar to Window's parental control, which allows site blockage and download blockage?
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
I think this is a great question, and shows that you care about your children.
That being said, most people using Linux will think of you as a freedom-stifler for even suggesting such an idea.
I personally feel that if you really cared for your children you would do one of three things:
All of these personal qualms aside, I think I have a few solutions for you:
try looking up "whitelist" and some linux terms to find info on how to effectivly control internet on a PC with linux.