The first thing I noticed is that her shoulders turn front shoulder in torwards the plate,back shoulder torwards the 3rd base dugout,I think she needs to learn how to get her negative move or walking away from her hands and not turn her shoulders like what she is doing now.Her lower half or hips need to start her swing first,her hands need to go after the hips. thats my 2 cents.
I went back and looked at her swing again for some reason the video is hard to load on my PC.But I agree with you,on the hips now that I had a chance to watch it more.Her lower half does goes first. I agree with rest of what you said, as I stated in my reply.
Her shoulders, hands, bat don't move until well after front heel is down, and the hips are starting to rotate.
I am not a batting expert, but I have stayed at a Holiday Inn Express one time, and I think your DD may have a hard time getting around on faster pitching because she 'overloads' when she turns in her front shoulder as her first move. Most hitting instructors I know prefer to do all 'negative movement' during the load, so that the first move on the swing is to the ball.