I've seen a short, lightweight woman use a Remington 870 20 gauge to very good effect in a recent training class.
Some may snort at a 20 but I've heard it has over twice the energy of a .44 Magnum.
I would see if I can borrow some kinds of shotguns for the wife to try out with birdshot, slugs, and buckshot. If you can get some competent help to teach her, that would make the experience positive. There's something about spouses ....they make horrible firearm instructors for each other!
Failing that, what I've told women is
-Keep the firing side elbow as high as it will go. Watch this because the elbow wants to droop during a shooting session.
-PULL the buttstock into the shoulder pocket HARD.
-Lean forward aggressively. For some reason many women don't lean forward in fight mode too well. Leaning forward doesn't mean put your hips forward; rather put the support side foot way forward with that knee bent and the firing side leg straight and driving back into the ground. Shoulders leaning forward of the hips.
-After doing the above 3, then show the basics of front sight, trigger press, follow through, etc.
If it's a pump then she should learn to rack the slide HARD and FAST right off the bat.
If she likes semi-auto shotguns, the 11-87 20 gauge is supposedly a VERY light kicking choice.
Finally, choose some ammo like Remington reduced recoil slugs, not the 3 1/2" Magnums.
If you can find a professional instructor, that would help immensely. The best defensive shotgun instructor I know of is Randy Cain
www.guntactics.com though I also hear Louis Awerbuck is incredibly good with scattergun training.
As a complement to the handgun, I think shotguns have a very useful role in home defense. I strongly believe that long arms are much easier to aim than handguns unless you get to about 3 feet or less. From where I lounge in my house usually, it's about 7-10 yards to one entry point. That's stretching it for a handgun under stress, but a snap for a shotgun. Also, once I was in my garage when someone drove up and approached me (total stranger!) asking for directions. Nothing bad happened, but the distance from where I was in the garage to the driveway was much farther than simple handgun range.
The shotgun and handgun don't replace each other in home defense. They support each other in overlapping roles.
Hope that makes sense.
Edmund