we decided to try one last time on Sunday with another email address, this time Gmail.com. It worked.
I did have a similar problem with Apple passwords sometime in the past; however, it took me all of ten minutes to realise that all I needed to do was to use another email address. How come it took you so long? Number one priority for Apple is online security. It is famous for it, OSX is the most stable platform and, even now, the risk of infection from malware, provided you use the appropriate tools and firewalls, is small. The fact that you had difficulty with your password suggests to me that Apple is rightly concerned with security. I have no problem with that. Still, well done for, eventually, solving the problem. Now you've learned a lesson perhaps you'll stop knocking Apple and revise your own working methods.