Years ago I wanted to get my best friend into shooting so she'd go to the range with me. The first time I took her she shot one round and that was it. Not only did the noise bother her but also the percussion and felt recoil (the gun was a 9mm Beretta 92G). It didn't help that there was a guy next to us shooting a large caliber....sigh.
I only had 9mm, 45ACP, 357SIG and 38 Super so I went out and bought a 22LR semi auto (I use all kinds of excuses to buy guns....LOL). I can't remember, maybe a S&W or Ruger? Took her back to the range during a quiet time and I shot the 22LR first so she could see/hear it. I asked if she wanted to try the 22LR and she agreed so I showed her how it worked, etc. It was love at first trigger pull. I couldn't pry it out of her hands!!!!
After that, when we were at the range I would ask if she wanted to shoot any of my other guns and she said no, so I let it alone and just let her shoot the 22LR. One day I was shooting my Colt Special Combat 1911 and she was watching. I asked if she wanted to shoot it and surprisingly she said yes (it was a gorgeous hard chrome gun and drew her attention). I showed her the manual of arms, had her load one round in it and fire at a target 7 yards away (oh......we shoot at indoor ranges). She drilled it in the bullseye, turned her head towards me and said "I really like this one"!!! Needless to say she had her own Colt Special Combat 1911 (hard chrome) two weeks later. She really liked the "slow push" of that 1911 compared to 9mm.
Next she got a 9mm Glock and her Texas CHL (LTC) and the rest is history. She doesn't do well with double action trigger pulls due to weak hand strength (arthritis) so we had to make sure she could rack the slides on whatever semi-autos she wanted to purchase.
Long story short........I tried to find out what she was comfortable with, didn't pressure her to try what she didn't want to, slowly moved into "louder" situations at the range, made sure she had really good hearing protection, went real slow.....I guess the main thing was that she felt comfortable and was having fun. You may have tried all these things but sometimes it's just a thing between husbands trying to teach their wives.....
She loves to shoot my 22LR rifles and hates my AR15s. So guess what......she shoots my 22LR rifles.
By the way, I'm a woman so maybe that helped ease her initial fears or maybe it was that I tried to make her feel comfortable and didn't push her, I don't know. But sometimes it just takes time and the ability to accept the limitations the other person may have.
If you are ever in the DFW/Carrollton area let me know and I could meet you/your wife at the range with a few 22LRs that I have (with suppressors, now THOSE are QUIET)!!!! I have tons of ammo so she could shoot as much as she wanted!!!
NOTE: you said she is shooting a Ruger LC9S......that would be a difficult "starter" gun to learn on for a "newbie" in my opinion. It's small to hold on to for starters and the felt recoil of a subcompact 7 round 9mm would be unpleasant for a beginner (heck, even I hate them). My friend would probably not have hit the target with a LC9S at all either and would have quit on me!!! Like most have suggested......start out with an easy 22LR semi auto and let her have fun with that for awhile (or as long as she wants).
"You may find me one day dead in a ditch somewhere. But by God, you'll find me in a pile of brass."~~ Tpr. M. Padgett