Is logged in as you. That's going to create issues beyond this.
On the kids phone you need to first setup their own account (google) and then do the change on the phone itself. https://www.groovypost.com/howto/remove-change-google-accounts-android/
I would be guessing why this other phone is logged in as you.
I just got a S9+ to upgrade from my old iPhone and created a google account and moved all contacts across. Now the issue I have is one of my kids has a S5 as a hand me down and the contacts have shown up on his phone and it has my name at the top of the contacts. The google accounts for the two phones are different but the data from the S9 seems to have hijacked the S5. How do I get rid of my contacts and connection to the S5