Macrodroid/Automate/Tasker and Syncthing.
I do something Ike this - we have a folder on our phones kept in sync with Syncthing.
Then use Macrodroid to save the info to a file (location, wifi name, wifi key).
Would probably require 2 macros - one to save the info, and one that looks for the wifi ID in the file when your phone sees that wifi as available.
Or just use a text file in that folder, keep a shortcut to it on your home screen. Whenever either of you update the file, those changes will show up almost instantly on the other phone.
If you ~~had~~ add a pc at home to the sync job, you get a little more stability in the sync (don't have to wait for both phones to be on to sync).
Wifi ID alone is probably all you need to save. Location would be superfluous (nice to have but not required).