The smaller gauge is worthwhile, but moreover, a gun that is the proper length of pull and fit for the ladies is paramount. Most of our 14" plus L.O.P. target guns can be just too much to handle for the smaller gals .
Get her her OWN shotgun. Great impetus to learn how to shoot it, and it isn't your old hand-me down stuff !
A Browning Gold Superlight Micro in 20 ga. may be an option. At just a little !over 6 lbs. it shouldn't be too heavy, and 20 ga. semis don't generate a lot of recoil with target loads. It is a little shorter in L.O.P. than standard Golds, but can be shortened even further.
Really want to teach your wife to shoot ??? Just like teaching the missus how to drive - you're way better off to get someone else ( who is patient & proficient) to be her shooter-coach ! Gracious, you wouldn't want her to learn YOUR bad habits, would you ?