I would avoid buddy press, it adds a whole other layer of complexity, rather check out a WordPress Groups plugin like this one https://wordpress.org/plugins/groups/.

If you’re keen on getting your content out there, sign up on http://ssg.space/ (new startup community/blog feed)

You might also be keen on trying Slack as a personal social network or tight knit community. I definitely think it could work in a family environment. They have Android and iOS Apps available as well as Mac and Windows app and of course browser based so it can really work like a cross platform private network.

You can try free first then upgrade to paid, never see ads and it’s always private.

If you’re keen on seeing it in action sign up for SSG slack group: http://startupstudygroup.com/slack/

I’ll also send you an invite for our incubator’s community, it’s still quite small though.