This extension disables Private Browsing, hides all the PB menu items and disables the keyboard controls, disables the clearing of browsing history, and the extension doesn't appear in the Add-ons except for the Firefox SafeMode.
https://addons.mozilla.org/en-US/firefox/addon/disable-private-browsing/

thanks, that is helpful, but if I am looking to keep the internet safe for my kids, would the safemode be more helpful? What does that do and can you direct me to how to add it one as well?

The Firefox SafeMode has nothing to do with "safety" or parental control.
http://support.mozilla.com/en-US/kb/Safe+Mode

"Safe Mode is a special Firefox execution mode that can be used to troubleshoot issues in Firefox. In Safe Mode, you can reset some settings or disable add-ons that might be the source of the issue. By comparing Firefox behavior in normal mode to its behavior in Safe Mode, where various items are disabled, you may be able to diagnose issues. "