how do I reset a child's password within family sharing?

Apple has the WORST user and password lifecycle management in the entire industry- I have seen enough to state this confidently. Even the local grocer trying to expand his franchise has better password management.

You can reset the password of young children with Family Sharing. When you create an account for a child, the password recovery email address is set to the email address of the family organizer. So going to http://appleid.apple.com and choosing Forgot Password will send the password recover message to the family organizer, not to the child.

Older kids (generally between 13 and 18) still receive their own password reset emails, or can answer the Security Questions to reset their password.

Family Sharing and Apple ID for your child - Apple Support

Once you have found that child Apple ID (Email address go here)

https://appleid.apple.com/#!&page=signin (And click forgot my password)

Hope this helps, best of luck to you.