EmmaJ,

You might have missed this in the earlier posts in this thread, but someone else (apologies to whomever I am failing to credit right here - they posted it even before sparky above) correctly pointed out that you can accomplish the same thing as private browsing by deleting the history and emptying the cache. Both of these options are found in Safari's menu items. If your children are as savvy as you imply, they will figure this out in no time and you will be back to where you are now.

I would advise following Las_Vegas' suggestion above and creating a separate account for your kids to use - one that doesn't have administrative privileges. Also, I'm not sure how the computer arrangement works in your house, but there should be no reason why they can't do their computing and surfing in common areas of the house where you can walk by and observe what they are doing. And I would recommend specifying the amount of time they are allowed to be on the computer - don't let it be idle time (idle hands, etc, etc) - if they are not on the computer for a valid reason, then it's time to get off. Just some suggestions from one parent to another.