I've never seen a mixed gague shotgun manufactured ...
Its a Big Safety Issue - and I think it's a really bad idea ! But you could do it with "tubes" - leave one barrel as a 12ga / put tubes in one barrel as a 20ga. But it is strictly prohibited by rule, on Skeet and Sporting Clays.
A far better idea - you could effectively do the same thing by changing your shells in a 12ga. Leave it as a 12ga - Load one barrel with 1 1/8oz, load one barrel with 7/8 oz ( like a 20ga load ) - or with a 3/4oz load like a 28ga. At least then, it would be safe.
That way one gun / becomes a gun both you and your wife could shoot safely / and there would be no tubes involved - and no safety issues ( because there would only be 12ga shells in both of your vests).
About a month ago / at a local club - we had a shooter blow up a 12ga O/U gun because he dropped a 20ga shell into one barrel ( then thought the gun was empty, and loaded a 12ga shell on top of it). He was with his grandson / kid was shooting a 20ga ...and his grandpa blew up a nice Beretta ( but noone was hurt ..) except his ego and $ 2,500 out of his checkbook.