ElCap 10.11.4 is screwing with my iCloud login

Since recently uploading the newest version of ElCapitan I am challenged each time I try to go to mail using my MacBook Pro, told that I must use my "device" to allow for use by an unknown device. Then the allow screen pops up on my my iPhone and iPad, yet I get no option to type in the code.

If I log in with Chrome instead of Safari, I get the same message but at least it gives me the code to type in.

But, sure enough, the next time I try to login on my MB Pro the same thing happens - no matter which browser I'm using.