Hi @timconsidine I hope you can get back to your family soon.
The 3 I'd suggest are Matrix, DeltaChat and Briar.
I'm aware that support and infrastructure been created for people inside Ukraine (and those who need to communicate with people in Ukraine), in the case of external Internet access being disconnected.
These servers are for Matrix, and Deltachat.
Right now, I know there are 3 different Matrix servers hosted inside Ukraine - Kharkiv, Odessa, and Kyiv.
DeltaChat is essentially instant messaging over email which then communicate via specific generic email servers. A user sets up a server by scanning a QR-code, then adds the people they want to chat with. It is localised to Ukranian and Russian.
Right now, there are 3 DeltaChat (email) servers hosted inside Ukraine - Kyiv, Kharkiv, and Odessa.
The last is Briar messenger. It is a messenger app for Android, Linux and MacOS (the mobile device version is most "featureful" supporting 1-1, group messaging, the Mac OS and Linux clients support 1-1 messaging only).
There is no server infrastructure required, it is peer-to-peer. It uses different peer-to-peer transports like the Tor network, Bluetooth, and the same local network. If you'd like to try out Briar with me, let me know, I use it.
There's webpages (in English, Ukranian, and Russian) with all the info for each city Kharkiv, Kyiv, and Odessa.
Another option to not forget, but often forgotten in the "Internet focused" world, is communications via licensed amateur radio operators. You'd obviously need to know a licensed operator where you are and in your family's city but much more robust in terms of dealing with censorship/breakdown in IP based communications. I'm assuming you're in the UK so RSGB.org is the UK amateur radio society. Unsure of the Ukraninan equivalent. Not something for immediate need, and I hope you won't need it in the future.