Certain SIM providers require APN settings to be adjusted on the phone in order for mobile data to work. Google family link can block these settings.
To get around this issue, you need to temporarily remove your child's Google account from the phone.
STEP 1: Remove your child's Google account from their phone
1) Tap settings on the OtherPhone home screen
2) Tap accounts
3) Tap on your child's account
4) Tap 'Remove account'
5) Tap 'Remove account' again
6) Click 'Can't find code' and follow the instructions on how to find your code
7) Enter the code to remove the account
STEP 2: Adjust the APN settings as outlined by your network provider
STEP 3: Re-add your child's Google account to the phone