It certainly is a valid use-case, but if you want something that is simpler to manage, look at pleroma and the Soapbox frontend. Pleroma takes way less resources and you'd be able to run on a Raspberry PI.

Another thing to consider, though, is to not run something like a social network and instead just get matrix and create group rooms for your family? Everyone would still be able to share updates and even call each other. Not only you eliminate the need of Facebook, but also WhatsApp/Messenger.