I want to remove the child’s account from my family sharing account

Re-read the document Move a child to another group using Family Sharing. It is unambiguous: You can't remove a child under 13 years old from your family group, but you can move them to another group or delete their account.

In the above page Find out how to delete a child's Apple ID is linked to the support document How to delete your Apple ID account, which says:

Can I delete my child’s account?

If you are the organiser 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 second option - the child requesting an account deletion - would apply as you indicate that you wish to continue your own account.

If the child is under 13 years old you must Move a child to another group using Family Sharing.

If the child is 13 or older you can use the steps in Leave Family Sharing.