We have a Nest Doorbell (battery) which is linked to my Google account, so it appears under Google Home on my phone, along with our Google Home Mini / Nest Mini speakers. I added my wife as a member of the household (Settings in the Google Home app) and as a result, if the doorbell rings the notifications come through on my phone, the speakers, and my wife's phone too. So, I'm guessing if you edit your Google Home settings so you and your wife are both members of the household, and the speakers and doorbell appear in there too, it should work the same way for you.
My Nest Doorbell (battery) is linked to my Google account and is in my Google Home (along with Google Home speaker and minis). We do get the notifications on my phone and my wife's phone but not on the speakers. It is weird and I cannot see how to make this happen.
That sounds really strange because the notifications worked on all of our speakers and both of our phones right from the start. Do your speakers work for other things, like playing music, Google searches etc.? Also, do they show up in the Google Home app along with your doorbell under the same "home"? It might be worth rebooting the speakers (or resetting them - perhaps try doing one of them first if you have multiple) then ring the bell and see if that fixes it because there are no options in Google Home to change how the notifications work with speakers - they should just work.
My speakers (original google home and a handful of minis) all work for standard stuff: playing music, timers, searches, turning lights on and off. But only the ringing of the doorbell is played on the speakers, no other notifications.
Thanks for visiting the Community.
Since this thread hasn't had activity in a while, we're going to close it to keep content fresh.
We hope you were able to get the help you need but if you're still having trouble, you might want to check out this link for additional information.
If the issue persists, feel free to submit another post, and provide as many details as possible so that others can lend a hand. Hope this helps!