I think it may be fixed!
I got so disguste with the issue I called AT&T and got hold of a person rather than having to deal with the lame chat support thing. The guy was in India but he understood what I was talking about - Outlook and Mail both nagging for the password (authentication errors). He told me how to fix it and his simple FIX worked.
He had me quit the mail app. He then had me log into the Yahoo site, the open Mail but said do not click on anything. Then he had me go to the top left of the Yahoo page and click on the Yahoo "Sign Off" button then restart the Mac. I did and after the restart Outlook popped my wife's mail.
Too bad the other ATT support people do not know about this simple tip that WORKS!
Shortly after posting that everyting was working okay my wife could no long pop her mail with Outlook on the MacBook Pro. The POP settings were correct but she was getting the same old nag note that there was something wrong with her user ID or password. I got an appointment with the Genus Bar and it was doing the same thing in the Apple store. Her iPad mail was also not working. The tech at the Apple Store was really a Genius in that he FIXED Mail, Outlook and the iPad.
There was nothing wrong with my POP settings. He went to the Yahoo web mail page and changed my wife's account from the old Classic to the new Web Mail. As soon as he made this change at the Yahoo site, all Mail started working. He said the new Yahoo activates IMAP and that did the trick
I did not change my wife's mail from POP to IMAP but he recommended I make the change if Yahoo starts scewing up again
I learned something new to me today!