I'm seeing a lot of defensive skiing. All of her motions are stop motions, to keep her from going. She is using braking maneuvers to execute turns. During each turn, her arms and her upper body are being drawn backwards, as if preparing for an impact. This is causing a number of issues.
First, she needs to round out her turns and use her turn shape to control speed, rather than a skidding, braking motion. Currently, her turns are Z shaped, and do not finish across the fall line. Efficient turns will be rounded, and finish across the fall line. Because she is not utilizing turn shape, she essentially is skiing with a series of linked recoveries. She gets going too fast, throws on the brakes, then goes the other way until she needs to throw on the brakes again. This is a fairly inefficient way to get down the mountain, and doesn't allow for much ability.
Second, the tension in her upper body is throwing her out of balance in a number of places, and putting her more in the back seat than she wants to be. Because of that, she needs to break significantly at the waist in order to stay over her skis. From that stance, most dynamic moves are difficult if not impossible.
Now I'm going to throw some harsh reality at you, man. You have already said this is about as far as you can get her on your own. You're not going to glean the skills needed to help her progress by asking questions on an internet forum. I can spend the rest of the evening telling you about CoM's and BoS's and CoB's, edge angles, platform angles, balance, edging, rotary, pressure, active steering, strong inside halves, femoral rotation, foot squirt, fore aft balance, and a zillion other things. It's really not going to make a difference. In order to be an effective instructor, you need to have mastery of the knowledge, and you need to be able to impart it in a clear and understandable manner. If you would really like to see your girlfriend improve, you need to provide her with professional instruction. I know its pricey, I don't expect to buy a Mercedes for the same price as my Subaru.
I also say this to help you preserve your relationship. I have seen many, many relationships go south or get seriously damaged because boyfriend tried to teach girlfriend, or vice versa. Its just a bad dynamic, and never ends up well. I have been teaching for a long time, taught hundreds of lessons over the year, to thousands of students. I'll never, ever, EVERRR teach my wife a ski or snowboard lesson. I like her, and I'd like to keep her around.