Forget about the LCP and the P3AT. They have worse felt recoil than other/most 9 and 38 CCW's. The Bersa 380 and PPK are both blowback, and thus have similar felt recoil (IMO) to most 9 and 38's.
If you wife is new to shooting, maybe she just needs some range time to get accustomed to recoil. Nothing wrong with getting her a 22, like a P22, and let her get some range time with it. As she gains experience she might be ready to step up in caliber. And even if she does eventually go to a 9 or 38, the 22 will still be a valuable range/training tool.
Bottom line, if all you can get her to carry initially is a 22, let her.