Hi naira92,
We see you've created an Apple ID for your child to use with Family Sharing, but they have a different Apple ID you'd rather use instead.
Apple ID's for children under the age of 13 cannot be removed from Family Sharing, they must be transferred to a different Family Sharing group. As this is a bit of an unusual situation however, you may consider simply deleting that duplicate Apple ID. Bear in mind, any account details and data currently associated with that Apple ID will be forfeit in deleting it.
See more details about the stipulations of deleting an Apple ID below:
While we'd recommend reviewing the entire article to confirm this is an option you want to take, the section relevant to your Childs account can be found here:
"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. "
After the deletion of that Apple ID, you can add in their preferred one in the same manner as you added the initial one.
Cheers!