… this could get long… 
… and not all of it will apply, so read to see what might apply and ignore what doesn’t.
BTW… sometimes what guys think we care about, and what we actually care about, are different. This is often a surprise to the guys. 
Don’t be too quick to decide “that’s not it” or “that won’t help”. 
Treating it as a “girl thing” may help. Find a women’t shooting group - The Well Armed Woman, A Girl and A Gun, or a local woman’s shooting group and buy her - AND a Female Friend or Daughter or Sister if possible - a class / meeting /event ticket. Women do this better in pairs or packs - we’re social creatures, for the most part. (The NRA’s Women On Target events are useful, but they don’t build community and ongoing relationships, so that’s not what I’m talking about here)
Even though this is a serious topic, we’ll do more of it it if we’re having fun. Since we often choose to spend our time on what’s fun to do rather than what we should do, you want to consider why it’s not getting her willing participation.
If she’s not into it now it may be because there’s some latent fear or anxiety, or it seems like too much work, or it just isn’t fun or rewarding. Hanging with other women to do this, and working with women instructors is the best way I know of to fix that for most women. Granted, some of us like shooting with the guys, but learning and talking with other women can really put us at ease, reduce our anxiety about what we do and don’t know, make it easier to ask questions, expose our lack-of-knowledge, take risks, and open us up to becoming more confident more quickly.
Once she’s having more fun with it, and especially once she connects that fun to the real-life value of those skills, she’ll probably be more willing to play. (Notice I said play… it’s important practice but fun important practice is better, even when it’s a serious subject). Once that’s happening, there’s time to take on the heavier, more difficult topics.
When you’re practicing together, find more ways to make it fun. If she’s competitive, how an you do that as a competitive game? (I like dueling trees - my hubby can kick my butt, but if he shoots left handed… 
) If she dislikes competing with you, or if it seems she can’t win and that’s discouraging, look for a cooperative way to practice. (maybe… you shoot a spot on the target of your choice, then he tries to shoot your bullet hole.)
A few other stray thoughts:
- Sometimes it’s because the gun really isn’t working for a person - consider that maybe exploring a different gun might yield a better experience… if it hurts, or it’s scary, or it’s difficult, or it’s hard to see progress, sometimes a different gun can fix or improve those things.
- Sometimes its an environment thing. If the ladies room at the range stinks, or there’s no place to sit, it may be someplace she doesn’t look forward to going. Consider changing ranges or improving conditions, or figuring out what you can do to improve the things that are irritating.
- Sometimes it’s a couples thing - learning from and training with someone you’re married to isn’t always successful. Getting an independent teacher, especially a woman, makes a world of difference for many women.
- Sometimes there’s an emotional underground current - taking this seriously might mean thinking about things that are difficult - like what if your kids were hurt or what if you had to actually shoot someone. Working with a women’s group or female teacher is a good way to help flush some of those issues out into the light. Some of these things are more difficult for women to discuss with men because we bring different emotional responses to those issues. Once that territory is explored it gets easier to discuss it with the guys we are attached to.
- Sometimes its a listening thing. My hubby wants to take all the guns all the time and shoot everything. I don’t. If I’m done, I don’t want to stay and shoot 6 more guns I’m not interested in shooting right now. If he presses that subject, I don’t leave the range happy, I leave the range annoyed. That doesn’t make me look forward to the next trip. When he remembers that I’m there for my reasons and that may not be the same as his reasons, we have more fun. He can shoot all 900 guns in his lane, and I can practice with the two I’m training with in my lane, and I don’t need to shoot the other 898 guns at all. He leaves the range satisfied and I leave the range happy
The last thing I’d say is … ask what’s working for her, ask what’s fun, ask what isn’t… and LISTEN to the answers. They might not be at all what you think.
BTW, there’s quite a few knowledgeable women on here, and some of us are teachers - any of us would be more than willing to talk with her to help figure out what’s working and what isn’t, and to help in any way we can.