Welcome to Apple Support Community!
It does seem that possibly you setup Apple Cash family after your child already had an open Apple Cash account.
you would need to contact Apple Support and speak with an Apple Cash Specialist on closing your Childs current account, then turn off Apple Cash in settings and turn it back on.
If the Account has been closed, then attempt to just turn off Apple Cash and back on.
Settings > Wallet and Apple Pay > toggle off Apple Cash and back on > tap on Apple Cash card and complete setup.
then everything should work!
Hope this helps ;)