I have taken a lot of flak for this piece of advice, but I am going to give it again anyway
I have EHK and had the same problems that you are talking about with your daughter. This is what the doctor's at U of M told me to do and it's something I still do to this day.
Take a regular shower. After toweling off, apply a mix of oil and water just to lubricate the skin and hold in some moisture. I then put on a pair of damp/wet cotton pajamas and then one of those plastic sauna suits over that. I sleep in that all night and when I wake up, the skin just ROLLS off of me. I usually have to spend a little time in the shower scrubbing myself clean, but it's like having brand new skin. I do it on weekends because I am usually a little tender for a day but it works and it works well.
On small children, I recommend doing either the top or the bottom, but not both because this can be a little dehydrating. My mom always made sure that I had water by my bedside and that I stayed hydrated. Yes, it's annoying and uncomfortable but the results are worth it for me and last for weeks at a time.