Delete private browsing in firefox??

No need to delete it, you can disable it.

http://support.mozilla.com/en-US/kb/Private+Browsing
via http://www.google.com/search?client...oe=UTF-8&redir_esc=&ei=cOObS8DkBoeG_Aa5l5T7CQ

 

Install an older version that doesn't have it or use a different browser. The things that private browsing does can be manually done anyways so just having the feature gone wouldn't fix your problem. If you have a problem with how someone is using the Internet, then talk to them, don't try solutions like this because it won't help in the least.

 

What about Parental Controls?

Or do you want to spy on your children's www activity?

There might be other software that logs www activity despite Private Browsing deleting the history.

Another possibility would be to tell us what exactly you want to achieve with deleting the Private Browsing feature, so maybe some users might be able to help you.
Proper help can only be given with proper communication, and you have children, so you should know, that communication is key.