You need to add your family members to your home in the Google Home app. No need for separate Sonos systems and/or Google homes.
First, make sure all your family members have a Google Account in order to use Google services like Home and Assistant.
Then, follow this link: https://support.google.com/googlenest/answer/9155535?hl=en#zippy=%2Cinvite-members-to-a-home Scroll down to the section titled “Invite members to a home” and follow the steps. Your family members will have to install the Google Home app on their phones to accept the invite they will receive per email.
After all this, every single family member will have to set up Voice Match by following the instructions on this website: https://support.google.com/googlenest/answer/7342711?hl=en&co=GENIE.Platform%3DAndroid
This is so the Google Assistant can tell you apart by recognising your voice and play music from each person’s Spotify account separately. Each one of your family members will have to do this using their phone with their Google Account logged in to the Google Home app.
Each family member will also have to link their Spotify account to their Google Assistant. You’ll find instructions on how to do this here: https://support.google.com/googlenest/answer/7551876?hl=en&co=GENIE.Platform%3DAndroid
After you’ve done all that, everything should work.
Note: When setting up Google Assistant on Sonos speakers (not Voice Match, but adding Google Assistant to the speaker itself for the first time) that don’t have voice control enabled yet, always make sure you do this using your own account. Otherwise speakers might show up in the Google Home app as duplicates.