Oh man...if I let her off leash she'd kill herself. I know because it happened a couple of times. Even on a relatively flat area at the end of the run, I let go of the ropes and she just started cooking it (I guess it was a little steeper than I thought). She has no concept of turning or stopping so she would have slammed into the lift but for the fact that she sort of went toeside and fell down.
At that age childeren progress vary differently. It is easy as an instructor to doubt a lesson given by anyone but them. But until you are out there with the same student it is just a bunch or WAG(wild ass guessing) if the lesson would have gone differently. If she doesn't have the concept of speed control yet and stopping I would keep her on the harness. a hoola-hoop can work better, but it sounds like this might be a little to close for your ability level right now. Just keep getting her out on the slope and lessons every once in awhile and as long as she keeps having fun that is all that matters. If you are concerned about the level of instructor you can always ask if a snowboard instructor with a "children's accreditation" is hired by the mountain and could go out with her. The accreditation is even more specific knowledge for working wiht younger children like your daughter.
P.S. great pics