My wife did not warm up to shooting and firearms in general until I started showing her the world of competitive shooter, specifically USPSA pistol. She was really drawn to the idea of competition and shooting as a sport and gave. Prior to competitive shooting she saw guns as a strictly violent affair.
+1 on the .22 lr and taking her out to pick what she wants. The M&P 15-22 is a pretty good place to start looking. Also consider having someone else "teach" her, sometimes it can be difficult to take instruction from someone very close to you. And finally, find a way to empirically show her improvement.
Good luck, I can tell you that the getting my wife to share the sport of shooting with me was extremely rewarding.
GU
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