Receiving SMS messages only in email

Strange, then either you had used the Gmail address as your Apple ID at one time, or had it as an available contact point in iOS, or your wife typed in your Gmail when initiating the first message in the thread (can't think of any way it would happen otherwise).

In any case, you might have her delete the thread and start over, this time selecting your phone number.

Alternatively, you can add your Gmail address as a contact point. Go into Settings and at the top tap on your name (very top of Settings) then select "Name, Phone Numbers, Email" where you can add the Gmail address, then go back to the Messages Setting I mentioned above and add Gmail as a valid way to reach you (but not send from). That may allow her messages in the existing Message thread to come to your iPhone.

You're welcome, good luck!

On your iPhone, go to Settings/ Messages/ Send & Receive and:

(1) Make sure that both your phone number and email are selected for "You can be reached by iMessage at". This way, any incoming iMessage to your Gmail account should come to your iOS devices (and not Gmail, unless that's something new I've never experienced, though people tend to reach me by my number).

(2) Make sure that your phone number is selected for "Start new conversations from". That way any new message thread you start originates from your phone number. Otherwise, subsequent replies may come to your email even if you change this setting later.

On your wife's iPhone there's really nothing to do, but if the problem continues after doing the above steps you might need to have her delete the thread between you two and start a new one, ensuring that she selects your phone number when initiating the message.