two Apple IDs

I have an old Apple ID that was used for iTunes, iCloud storage purchases. Also, have a new one that is primary for a new Mac, iPhone. The old one was used by other family members for app purchases.

I am trying to change the "old" Apple ID to update some credit card information to insure continued coverage. However, it is beyond frustrating to try and change it from my primary Mac, iPhone as they keep trying to change my primary Apple ID. When I try and do it via web browser, I go down a path where it tries to ask for an old credit card...and authorization code as means to validate the account. That card is dead, having been compromised...and a reason why I have to update the old ID card info. Don't have the authorization code to enter, so stuck. What do I do to change the old ID PW so I can update the old card info?