Hi Geoff K,
"An aside; Why does the Apple spell check not recognize iCloud, iPhone, or iMac?"
Amusing observation. I had not noticed it; I use a browser-native spell check.
As I understand you, you have an AppleID that you use for various Apple services that you wish to change the password for. In trying to do this, you created another AppleID. I would recommend ignoring this newly made AppleID and focus on using the first. There's - as I understand your story - no reason to switch to this new AppleID and it is not possible to transfer your purchases between the old and the new AppleID. Keep with the old is my advice.
What you want to find out is what the AppleID's username is. Generally, this is your mail-address. If you have a mail address that you receive notifications on iTunes purchases or iCloud invitations, that is likely the username you are using.
Go to appleid.apple.com , use 'Manage your AppleID' and login using your username and the 'unsafe' password. To the left, you'll have 'password and security', you'll be asked for your security questions and be able to change your password after verifying them.
If you have forgotten the answers to your security questions, reset your password at iforgot.apple.com and contact AppleCare Phone Support to reset your security questions. This is assuming you have not yet set up your two-step verification process.
If you have any questions, please feel free to ask. Please do not post your email address here.
Kind regards,