how do I change my child's Apple ID for family sharing

You don't need to change the ID to add them to Family Sharing.

Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

See the Apple Support article(s) below. Click on Apple ID Name Change.

Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.