Two-Factor Verification

Well, to start with, there is two-factor authentication and two-step verification. There is no such thing as two-factor verification. Which one is it? (I know it is confusing, I didn't make it up.)

Two-factor authentication for Apple ID - Apple Support

Two-step verification for Apple ID - Apple Support

Switch from two-step verification to two-factor authentication - Apple Support

Confirm which feature you're using

If you're not sure if you set up two-factor authentication or two-step verification, use these steps:

1. Sign in to your Apple ID account page.
2. In the Security section, look for two-factor authentication or two-step verification, then see if the feature is off or on.
   

If two-step verification is on, continue with the steps to turn it off, then turn on two-factor authentication. If two-factor authentication is on, then you're already set up.

See Two-factor authentication for Apple ID - Apple Support

Your secondary trusted phone numbers would only come into play if you are using the AppleID recovery system, or click the "didn't receive a code" dialogue box if a code did not come through when using your trusted number or device(s).

I don't know if you and your wife share an Apple ID or not, but I share mine with my granddaughter and the code only comes to the "Primary" iPhone number in your iCloud. This is not a big problem in that their is a check-box on the page where you enter the code that allow you to only enter the code once and then the device is good. If my granddaughter receives the code she messages it to my device and I check the box and then enter the code.

Why don't you try asking the questions...