What happens when you try to add your daughter? Error message(s)?
Since deleting the son's second account, have you tried signing out of iCloud, restarting the device/computer, and then signing back in to see if that helps?
If necessary, contact Apple ID Support for assistance. See the Apple Support articles below for contact information.
Apple ID - Official Apple Support. -
Contact Apple for help with Apple ID account security - Apple Support. * (Link doesn’t always load)
Get Support - Work through the screens to get a chat option. You may have to pick a slightly different problem.
Apple Support schedule phone call. -
Apple on Twitter
From the Apple Support article below.
Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.
Security and your Apple ID - Apple Support. *