@equusalbus78 

To be honest this would most likely be a setting within the Google Home account.  That is because the integration of Kasa into Google is a cloud-to-cloud interaction.  There is a single Kasa account that is linked to the Google Home account and allows voice control.  

I would suggest contacting Google and see if they can walk you through the restriction settings to see if something like "3rd party apps" are being blocked.  If so its possible they can walk you through enabling the Kasa app for the child's account.