This girl needs to learn to stand in a centered stance, over the entire foot, with her shins in contact with the tongues, and then stay with that through the turn cycle. What the video is showing is some ability to move forward at turn initiation, but then a consistent habit of quickly sitting back. The result is a lack of force on the front ends of the skis, an inability to engage the edges in a carve, and turns that quickly wash out into accelerating diagonal runs.
You say, "Boot is a 2 buckle with the top buckle as loose as it will go while still buckled to help open ankle ROM." Most two buckle boots, especially children's sizes, are quite soft to begin with. To my eye, this girl is displaying quite a high forward shin angle at turn initiation at many points, for example at 16, 28, and 35 seconds in the first clip. I think it likely that the boots are adjusted TOO LOOSELY, so that she collapses forward in them and then must compensate by sitting back so that she doesn't lose her balance completely. We see this with many, many students. To repeat, hips back are often a symptom of boots being too loose, rather than too stiff.
On top of any equipment issues, if she has been skiing for a number of years, this girl is likely displaying the legacy of a small child stance that she never shook off. She needs to realize that she now has a stronger, more mature body, and is capable of standing tall and forward while skiing. This mental adjustment is challenging for many children.
With equipment appropriately adjusted, I would prescribe a practice program including:
1) On gentle terrain, straight runs starting parallel, and then repeatedly slipping into and out of a wedge. The goals should be to maintain a good stance throughout, to become comfortable and confident with that tall stance, moving aggressively down the slope, and to develop the ability to create good edge angles and put forward pressure on those edges, strongly engaging the snow.
2) Parallel traverses, with a transition into parallel J-turns starting from increasingly steeper downhill runs. Goals should be, again, a good, aggressive stance throughout, the patient creation of edge angles through knee angulation, and the creation of continuous, rounded, carved turns by harnessing ski performance.
3) Starting on a very gentle slope, linked parallel turns, with a strong focus on continuing turns across the hill as far as possible. A goal should be to continue each turn until the skis slow so much that they nearly, but not quite, stall out, and to move smoothly into a new turn in the other direction. If this girl is unable at first to perform this in a parallel stance, back off and do it first with with wedge turns.
She should initially perform these tasks slowly, on gentle terrain. She should develop the feeling of driving the skis forward by pressing her shins into the boot tongues.