I find my semi autos have about have the recoil of pump action guns.
I have the following:
Stoeger 12 guage with pistol grip
Benelli M1 with pistol grip
Saiga 12 converted to pistol grip
Also have a rem 870, has pistol grip, but not the spec ops stock.
I am not a great fan of shotguns for home defense, not because of the guns, but because few people will practice with shotguns for tactical situations.
I use buckshot and buckshot has significantly more recoil than birdshot.
Unless your wife is committed to becoming proficient with a shotgun, she may be better off with a handgun.
A 9mm or a 38special that your wife can handle is better than a 12 guage she can't handle.
Personally my home defense gun is a 45. Of course I have an assortment of shotguns I can access if the Colt won't do the job.