An even better idea, assuming she does want to learn, would be for her husband to take himself out of the picture as her teacher; that always sets things up for additional stress. It would be way better to have her learn from a professional in a women-only class -- ideally one with a woman instructor, but at least with someone who has experience teaching women to shoot.
Exactly right. And in addition, the fact that her father was a shooter tells you nothing
about her attitude to firearms and loud noises today. Or about being taught to shoot by a male. No assumptions. Offer to arrange the training as Vanya recommended. If she says no, forget it for now.
Lots of people, and not just women, really have an aversion to the activity we value so highly.