For a second season she's doing a good job. For improvement, I'm having similar thoughts as Josh and markojp.
She needs for her legs to turn more than her upper body, so her jacket zipper is pointed more down the hill than her skis. Repeat: her upper body (hips, shoulders, torso, all together as a unit) needs to be facing more down the hill all the time. Getting this to happen comes first before anything else at this point. There are numerous drills people can do to help them feel this happening. It's like doing the twist, only you twist below the hips - not at the waist - and you do it slowly and progressively throughout the turn. Figuring out which drill will work is what an instructor should be able to do in a private lesson. As Josh says, this separation of the upper and lower body is crucial if she is going to be able to ski from outside ski to outside ski, with her legs doing the work.
Her stance needs work. The way I describe it is "punched-in-the-stomach" skiing. She needs to stand up straighter, tuck that tummy in, bend forward at the ankles while keeping the heels firmly planted on the boot soles, and ski that way feeling the entire ski engaging the snow, tip and tail equally. She'll feel stronger balance immediately.
Since the video calls itself a carving lesson, I want to address that. There are several things she needs to own before she carves. The upper body/lower body separation comes first, along with the stance issue. But she also needs to focus some attention on how she initiates her turns if she's going to move up the skill ladder. That's why people are mentioning sideslips, falling leaf, and pivot slips. Those are all drills targeting initiations of steered turns. Most skiers learn to steer their turns before learning to carve, unless they go through seasonal programs in race training.
I second the advice to get her a private lesson with a seasoned and well-respected instructor.
Edited by LiquidFeet - 4/11/14 at 8:42pm