If you do it by email then your wife just set up an email filter to automatically forward a copy of any authentication email to your email account. Then you both get it every time. Problem solved for your situation.
Secondly, you can use an Authenticator app. This is what my wife and I do for our shared account. I setup 2FA with the authenticator app on Google Authenticator, then I took my phone over to my wife, and told google authenticator I wanted to transfer an account code selected export accounts on mine and import accounts on hers then I had her scan the QR code. Now she had a copy of the 2FA authenticator code on her phone with Google Authenticator app too! She no longer has to ask me for a code to log in to the Wyze account. She can simply get it herself any time she needs it (which is basically never because the app just leaves her signed in anyway).
Either of those 2 options will resolve your frustration with needing your wife to authorize you every time.