Why does Apple Watch only ring using wife’s iphone

"...We share the same apple id,.."

That should never be done and is the cause of this.

By one of you creating a new ID and starting afresh it will be less effort in the long run than constantly troubleshooting crossovers.

When you both have your own apple ids (or now) then on your phones...

Settings, Messages, Turn off iMessage 

Settings, Face Time, Turn off Face Time 

Restart the phone. 

Settings, Messages, Turn on iMessage, SMS, MMS 

Settings, Messages, send & Receive, select your number which should now be there. 

Settings, Face Time, Turn on Face Time 

What do you mean by "using wife's iphone"

Calling from it?

Paired to it?