First try wasn’t serving you good enough?
There is a good news about: Apple is slowly rolling out a revised system to let you use a second factor with iCloud and other services that use an Apple ID!
That IF you’re running the latest major OS release and the latest iTunes on every device connected to the same iCloud account. But you may have to wait for it: the system started rolling out in testing this summer for early public beta testers and developers, and started its full rollout a few days ago with the release of El Capitan.
Is the revised two-factor authentication available for your ID?
Check the infos HERE how to start!