The Nest does not sense or provide outside temp readings. The 'outside temp' that you see is pulled off a weather service on the internet, and displayed for your zip code. If you can remotely monitor each thermostat via your phone, you will know the Nest has a working internet connection. The next thing is to go into the Google Home app and make sure that both homes are listed separately and each has the full address and zip code.
If you have added both thermostats to the same Home, you will only get outside weather readings for that one home.
