Your wife is skiing with a rigid body. It looks like she worries that if she wiggles or twists or moves any part of her body she'll lose balance and fall. This kind of skier rigidity usually comes from insecurity about remaining balanced. As long as she skis that rigidly, she will not be able to try new movements that will increase her skill, her control over her skis, her line, and her speed.
So the first and most important thing she needs to work on is loosening up her body, discovering how much she can move her arms and hands and shoulders and legs and feet without falling over as she makes turns. I've never known anyone to be able to relax when told "RELAX!" So simply telling her to relax probably isn't going to get rid of that frozen pose.
Here is one suggestion for her:
1. Beginner terrain
Ski on the lowest pitch terrain available. Isolated beginner terrain is best. This should allow her to experiment with movement without intimidation.
2. Thumpers for weight on downhill (outside) ski
Work on skiing with weight focused on the outside ski. This involves lightening the weight on the inside ski. One drill that works well for this is "thumpers." While heading across the hill, between turns, lift the tail of the uphill ski and put it back down. Keep the tip on the snow. Do this lifting repeatedly. Lift the tail, put it back down with a thump. Thump thump thump the tail all the way across the hill. Turn, then thump thump thump across the hill in the other direction.
3. Your wife is aft. Thumpers helps skiers stay less-aft when they figure out how to stand on that downhill ski so they can lift only the tail of the uphill ski. When an aft skier attempts to lift only the tail, the tip lifts too.
4. To get only the tail to lift, she can slide her feet back, as if trying to get both feet behind her hips. The feel won't slide back that far, but the effort will hopefully get the feet farther back than they are currently.
5. She can work on thumpers all by herself; it's easy for a skier to tell if the tail is thumping or not, and if the tip is staying on the snow or not.
6. If she is afraid of lifting the tail of that uphill ski, she can work on lifting it only a half centimeter or so while going real slow.
7. Once she is used to thumping the tail across the hill, she can try moving the thumping up higher/earlier in the turn. Start thumping what will be the uphill ski when the skis are pointed down the hill. Then start thumping before that. This will be a big breakthrough!
8. Why do thumpers? It gets each leg doing something different, and it gets the skier to balance on the current outside ski, then shift it to the new outside ski. The rigidity will loosen in the process, and skiing from outside ski to outside ski will replace her current two-footed balance.
9. Shin-Tongue for getting out of the back seat
It's hard for a skier to confirm on their own that the feet have been moved back far enough to fix aft skiing. If the tail lifts without the tip when doing thumpers, that's one sign. Another thing people pay attention to is shin-tongue contact. Your wife can try to focus on strengthening that contact between the front of her lower leg and the boot's tongue. She can do this by sliding her feet backwards under her and keeping them there, not by bending the knees more. That only moves the hips back, and increases the "sitting back" aft situation.
10. Another way to confirm the feet moving back is to see if the tilt of the lower legs matches the tilt of the spine. These should match. An observer can watch your wife from the side, or take video, to confirm this is working. Currently, your wife's lower leg tilt is more upright than her spine. "Bending the knees" does not fix this; it only moves the hips back, and increases the aftness. Slide the feet back to increase the forward tilt of the lower legs.
11. Strengths
Your wife is skiing with good strong control of her speed using turn shape and line. Her turns are consistent. Bravo! She is looking ahead (not down)! She is skiing mostly parallel - great! She has a good strong base upon which to add increasing skills.