This is more of a firewall task than a browser task.

You really shouldn't be using IE either, for reasons of avoiding malware, viruses, and other Internet born nasties. I'd strongly suggest switching to Mozilla Firefox or Opera, the only two non-IE based browsers for Windows.

In any case, you should investigate various methods of "kiosk browsing" which should get you closer to your goal. Maybe even there, depending on how clever your kids are with technology.