Agreed. The animation looks to have too much side to side motion, like a dog waggling it's tail enthusiastically, and it's accentuated by the stiff skirt.
For hip drops think of the motion you'd get with a stringed puppet/marionette if you pulled only a string from the point of the hip straight up and then let it go. That's what is happening at the skeleton level. A live dancer has different ways of powering that movement and a variety of ways to change the feel of it, but as Kashmir says, the hip is dropping vertically.