Well because your original post was kinda misleading.

There are multiple things you talk about:

• “Ding-ding” notifications - well you can adjust notifications, to help with not developing an addiction

• her group chat - do they want to move their friend group chat to a fedi platform? Or were you just clumsily wording?

• family fedi server - that is what you are talking about now, and it’s a completely different thing. You could set up a closed-registration mastodon or vernissage instance for that, but tbh I wouldnt recommend using any ActivityPub software for the purpose of sharing private photos and messages with your family. Because there is always the danger of that data federating to all kinds of servers…