Aside from the recoil mentioned above, a lot of women can not manage to pull the slide back on a small automatic such as the
Kahr CW380 due to the stout recoil spring that the smaller guns require. You might take a look at the Glock 42 380cal. I had one briefly and the recoil was very managable. I don't recall that the slide was difficult to operate. Take your wife to a gun store or gun show and let her handle a variety to see what she likes.
Be assured tho, that the tiny critters, with a few exceptions, no matter what caliber, will have a significant recoil. One exception mentioned above is a 25 cal. You might have to search to find one, but Colt and a couple others made them some years ago.
You referred to her shooting a 38, presumably a snubby. I reloaded some soft loads
for my wife for her first shooting lessons as she like my Ruger LCR 38 revolver over the auto and her reaction to my telling her about recoil, was "whats the big deal". She didn't know the bullets had been downloaded to reduce recoil. The point here is, that even downloaded bullets will have more punch than a very small caliber, and if the wife is comfortable shooting that pistol, then you're ahead of the game.