Apple id verification error / family account

Hello. My kids use an iphone that I have set as a "family account". It asked for a different apple ID than mine, and a password. I was forced to create an @icloud.com account just for that. I wrote that account and its password among my others passwords. It worked, besides it's pretty complicated and far from intuitive. Now my son wants to download an app and the iOS asks for a password. I wrote it an it says is wrong (the same he has been using for downloading many other apps). I go to icloud.com and it says that the mail @icloud.com account doesn't exist. I just cannot understand this iTunes approach to make things complicated. Is there any way to reset the password? Many thanks!