I need to view the private browsing on my computer to see what my young child has been viewing.
Not sure how often
== not sure
Private browsing does not retain history, see https://support.mozilla.com/en-US/kb/Private+Browsing?bl=n&s=private%20browsing&as=q#What_Private_Br...
You need to use other methods like a router or firewall with a password protected logging feature if you want to see the history of visited website in a reliable way.
There are a lot of ways to clear the history and other private data in Firefox.