I'm not sure what you mean by "family link".
To add your son to your "household", go to Settings | Household in the Google Home app and select "Invite a person". Your son will need a Google (gmail) account, and when he accepts the invitation to your household he will have full access to everything. Google Nest does not have any limited access options.
Since my kids are now all adults, I didn't know there was a Google "Family Link app". I can't tell whether you can use "Family Link" to control access to turning on lights connected to the Google Home app. This is all I can find:
Thanks for the help, @MplsCustomer.
@Mstewart1979, thanks for posting. This is not the experience that we wanted you to have, let me help you out. From which country are you contacting us from? What message are you getting from your phone everytime you add your child's account? Is his phone connected to the same Wi-Fi network?
You can force close and reopen the Google Home app on both phones to refresh, Rebooting the phone might help too. If that did not work, try to uninstall and reinstall the Google Home app.
Let me know how it goes.
We understand. To make sure, what's the make and model of your son's phone? Even if your son is not a member of your household, he can still be able to control your lights via voice commands. If you wish to add him to your home structure, removing parental controls off your son's phone might be the only way.