I do not want to convert to the Google login. I am using 2 step verification on my account and it is working fine. Issue is when my wife needs to login to our account using the same user id and password as me the 2 step verification number comes to me. This is very inconvenient. How can I resolve this?
Well, first, I don't think there is any way for 2-step verification of a login to your account to come to anyone but you. That's exactly what it has to do.
Second, if you migrate your Nest account to a Google account (we did so a couple of years ago: https://support.google.com/googlenest/answer/9297676?hl=en), you can go to Settings | Household in the Google Home app and invite your wife to become a member of the household for your Google Nest "home/structure". She has to have a Google account and after accepting the invitation would then log into the Google Nest app and the Google Home app with her account. (The Google Nest app has/had an equivalent function under Settings | Family). Note that family members have full control.