Reading thru the posts it seems like you have a good grasp on the family type. I can not think of anything to add.
re: would be nice to inactivate the link for the name of the family, forcing people to click on individual members for more details.
This may or may not meet your needs but worth a try.
re: Probably need to change tabs to separate pages, too bad, tabs is definitely cleaner look.
Yes, I would recommend separate pages tabs can cause many side effects from putting the shortcode on the page multiple times. It’s doable as there are enough options in Connections to workaround most, but not all, side effects such as the resolving to the correct tab.
Hope that helps some!