How can I retrieve my "iCloud passcode"

We have 2 - computers a MP w/10.12.6 and a MP w/10.13.3 and two iPhones. My wife recently upgraded her OS to High Sierra discovered that our calendars were no longer syncing to her MBP. We went into System Preferences and in Accounts in Calendar Preferences discovered there was no account listed. We attempted to add an account and got stuck in an endless loop as follows:

A popup window that said "iCloud lets you . . . " and "Sign in with your Apple ID:" I filled in my email address and password and clicked "Sign In." I then received a 6 digit code on my phone which I entered in the 6 boxes on the MBP. I then got a screen that said to "Enter your Mac password to continue. I entered my ID and password which took me to a page that said "Your iCloud data is protected . . . " and "To access your iCloud data, enter iCloud Security code (a 6 box field). We don't remember ever establishing a 6 digit iCloud code so I clicked "Forgot Code?" and "Use Other Device".

Both of our phones were active for over 10 minutes and never received a code. What can we do.

This two factor process is a REAL PAIN. (The caps are to emphasis our frustration.) How can we get rid of the two factor process?