Would it work to block outgoing traffic at the router?

I forgot to mention, it’s easy to use, as it’s similar to every other messenger app, so even not so techy members can use it.

I’d recommend Threema. It’s privacy focused, based in Switzerland. You don’t even need a phone number to create an account, they collect no data on you (claimed, but haven’t checked) and the code is open source, under A-GPL 3 license.

There’s a build for Apple and Android, for which you pay once.

I use this to talk with important family members.