Hi Robert,
Welcome to the Moms Panel! We're glad you're hEAR!
Your trip will be here before you know it and I love that you are planning ahead. I haven't seen any restrooms labeled as "family restrooms" but there are companion restrooms in all of the theme and water parks as well as Downtown Disney. These restrooms are generally used for guests who need assistance from another member of their travel party.
Companion Restrooms are noted on the
Guides for Guests with Disabilities which are available at Guest Relations. You can also download a copy prior to your trip by clicking
here. You'll find the PDF files of each park located near the bottom right of that page.
There is a very reliable unofficial Disney site
www.Allears.net that has a complied list. Once your reach their site, click on the search option and type in "Companion Restrooms".
Wishing you minnie magical memories :-) Allison