Maybe you could use JS to "link" to the new page (for those that are JS-enabled, of course). If you use location.replace instead of the usual location.href, the old URL is replaced by the new on in the browser's history.
http://docs.sun.com/source/816-6408-10/location.htmBut none of this solves your problem. Daddy can click the back button twice and get to the page previously viewed which likely is on the anti-abuse site too. And there's always the cache.
While many browsers can be run in kioskmode where it's possible to disable a lot of things, it can be pretty complicated. If the kid is in a risky situation, I wonder if it wouldn't be better to use something like Off By One. It keeps cache and history in memory, nothing is written to disk. When the browser is closed, it's gone. You can run it from a USB stick or even a floppy. It won't make pages look pretty though.
http://offbyone.com/offbyone/