Try this new extension - Disable Private Browsing:
https://addons.mozilla.org/en-US/firefox/addon/disable-private-browsing/

Ignore the review that I made there on the 22nd, as two new, improved versions have been released in the last 6 days and most of the items I wrote about have been fixed.

Richie just needs to come up with the feature to disable clearing any browsing history, which he is working on.

Given some time on their own, your kids can install and uninstall a new browser such as Chrome in no time flat(I hope they are not reading this). A password-protected computer is front line defence, after that supervision is your only answer.

I'd better not mention trust or what you can do these days with a USB stick.

@alan_r

With a locked down user account for the kids to use, to prevent them from installing any programs at all, this is about as close to "perfect" as any one can expect. Compared to the other 3 or 4 attempts at "extensions"over the years since PB was added to Firefox, which haven't been updated (to the best of my knowledge) for Firefox 4+ versions, this is the best I have seen. There is still an unfixed Bug that hasn't even had a new comment posted in over 15 months, that deals with Firefox not "respecting" the Parental Controls in Vista and Win7 and that is what really needs to be fixed properly, to solve this problem once and for all.

I ain't even gonna address USB flash sticks and portable browsers, except to comment that the right type "glue" in a USB port won't short the contacts in there and if I had kids to worry about, there wouldn't be a usable USB port for them to use.

Fair enough! My kids are in their 40's and I keep a close eye on my grandkids on my computer.

When I had teenage nieces here and wanting to use a computer a few years ago, all they had access to was their grandmother's old Win98 PC which had very limited USB functionality - so no "stick browsers" and a stern warning from me not to install anything or they would both be washing my car and "mom's" for the next year. I have since fixed that issue with a "patch" I found on a UK website, to get the USB ports to work with USB storage devices. Makes it easier for me to to periodic maintenance from a USB flash stick, than having to burn an updated CDR every 3 to 6 months, and to back up the data on that PC periodically. I wish I could get my mother to even try a newer operating system than Win98, but the other computer she uses at work is a DOS6.0 PC from 1994 - no security issues as it has never been used on the internet and only has an old version of Word Perfect installed.

Thank you! I believe this will make me feel a lot safer. I know there are ways, there are always ways.. But like burglary - no matter how many locks you install, anyone who really wants to get in will get in. But the chances for anyone wanting to try are a lot smaller when stating - even only symbolic - that this door is locked - I do not want you to go in there!

With private browsing turned off, my kids must directly undermine my instructions - on purpose, with a lot of effort to go wherever not allowed on the internet, and I don't believe they will do that, cause now it's a real trust issue. With the private browsing option it was just too easy.

I really appreciated this solution, thank you!

You're welcome.