Few games from my experience:

Kirby's Epic Yarn (Wii) - although it uses classic console controller scheme, it's fairly slow and forgiving game, so she can train on it. With some skills developed later on you could then try something like Trine, considering it gives you ample time to figure out how to solve the puzzles and proceed.

I assume you've already tried out various Wii games, given that Wiimotes are easier to handle than classic controllers, so won't be suggesting anything like that (goes for PS Move as well).

Point & Click Adventure games are great playing together, if that's your cup of tea - while you don't really control separate characters, the whole process of figuring out stuff together is a blast. If you're up for something fairly light, yet very entertaining, try out Guilty Party (Wii).

Affordable Space Adventures (WiiU) - this is great coop game, you can do the "tricky" part of driving the ship, and she can control engines and other stuff onboard - working as a team is of paramount importance in this game.

If you have a chance to go to some VR Arcade, you could try playing co-op something like Arizona Shunshine or something similar.

Ultimately though - if she doesn't pick up on anything much, and keeps playing only occasionally, I strongly suggest boardgames - again, just from personal experience with few persons, people who are not that proficient at hand-eye coordination required for most video games or feel too much pressure coming from their real time controls, often tend to find boardgames just the perfect fit with the same (or greater) amount of fun - if you need any suggestions with that, just say.

Ignore those suggestions above try these 1-2 switch, snipper clips, or overcooked thank me later :) lol

If it makes her feel any better; I don't either.

Wii Sports, Mario & Sonic at the Olympic games, Kirby's Epic Yarn (can you even die in that game?), Mario Kart (begin at 50cc), Ms. PacMan (I don't remember if all versions had coop, SNES definitely had it), Pang AKA Buster Bros. for you americans, maybe Toejam & Earl.

Any telltale game. It's incredibly slow paced and will get your wife used to using and holding a controller.

It worked for me.

Overcooked 1-2
Little big planet, any
Fat princess adventure
Knights and Bikes
Lego games, Harry potter for example
Magika 2 after some experience maybe

I keep seeing Overcooked recommended, and while it's one of my all time favourite couch co-ops, I would really not recommend it for someone who doesn't have good skills with controller - game is quite frantic, often depends on quite precise placement and on top of that is time limited.

Until Dawn and Man of Medan can be fun. There's not to much "gameplay" besides the occational QTEs.

Also, try Hidden Agenda if she feels overwhelmed with the joypad. My GF liked that one quite a lot, since she can use her cellphone as a controller. There are actually quite a few games in the PS4 Playlink-series that can be played with the phone.

Tetris 99. Take turns.

I actually have that game. Forgot I had it!