Also, as addition: If you try to add a NEW laptop to the family account, remove your child from the family (family.microsoft.com), restart everything (computer/laptop you need to add), and then spend some frustration to add the same child again to the family. After some login here and login there, with both your account and your child account, things start to correct themselves.
Your account: Go to family account settings, and make sure the newly added child is part of your family, and allow access to the laptop/computer.
Kids account: Log in on the laptop/computer and log in at account.microsoft.com using Edge. That finally synced everything, and added the new laptop to the family overview in family.microsoft.com for the admin account. It can take a few minutes.
And... everybody is happy again.