Hello ayork,
Thank you for using Apple Support Communities. It's my understanding that your child isn't receiving emails for their iCloud Mail account. You've come to the right place! I'm happy to help.
If you haven't already, take a look at the following resource to make sure the appropriate steps were taken to add the email account:
Add an email account to your iPhone, iPad, or iPod touch
If the issue persists, the remaining steps in the resource below can help:
Get help using iCloud Mail
Let us know the results. Please include specific error messages and any other troubleshooting steps you may have tried.
Have a nice day!