Apparently this procedure posted on Reddit solved the problem!!!
Putting it here in case this may be useful for others too.
I did it the RESET only on my wife iPhone (not mine which is the home owner).
Before this, I also "removed" the home app from my wife phone and re-installed it back.
Then applied the profile reset below.
After some minutes of waiting, the invitation was received and she was able to join the home again.
download and launch the HomeKit reset profile Safari on both mobile devices (looks like they change the link periodically, so be advised link may be dated): http://appldnld.apple.com/iOSProfiles/HomeKitReset.mobileconfig (note: you can try first on just the one device and avoid full reset, but I was forced to do both devices)
install the profile on both devices then go to settings to install the profile per these instructions: Install a configuration profile on your iPhone or iPad - Apple Support
restart both devices (may be optional, but doesn’t hurt)
go to settings and scroll down. You should now see a “Home” icon to open then select to “Reset Configuration.” WARNING: this wipes out all your HomeKit accessories and settings. You will need to start over.
open HomeKit app on both devices. They said to leave app open for 10 minutes, but mine reset in a minute. This should force reset your configuration keys.
to test, I added a single HomePod mini to a new Home and then invited spouse. She accepted easy breezy.
It took over a month to get through support to this solution. Hope it saves someone some time and frustration. Good luck!
Credits to:
https://www.reddit.com/r/apple/comments/xwwv3b/apple_homekit_invitations_not_working_solution/