How do I access the site history from a family member's private browsing session?

You can't. See: http://support.mozilla.com/en-US/kb/Private+Browsing#What_information_is_not_saved_in_Private_Browsing

why does it say then, when reading about private browsing, that this doesn't prevent and employer to "see" or an IP where you've been?

Because an employer's servers generally track and keep a record of what you are doing on your work computer. Every outgoing connection is logged and kept by the employer's servers that establish internet connections for all of your internet usage at work. It would be very, very rare to have servers in a home set-up.

Thank you

You're welcome.