I would to delete my child’s account

For information on deleting a child's Apple ID, see the following from: How to delete your Apple ID account - Apple Support

Can I delete my child’s account?

If you are the organizer of your family, you can delete your child’s Apple ID when you request deletion of your account. Your child can also request deletion of their Apple ID, which requires your approval.

The approval request will be sent via email to the primary Apple ID email address of your family organizer account. When approving the request from this email, you will go through the process of deleting the child account.