Parents are desperate

[AcornsFalling]

I have had similar problems with my own daughter, who is also exceptional. She is now four and a half and it still turns into a power struggle at times.
I found two good resources- google dr. Laura Markham, she has a lot of Q and A on her website which may be encouraging for the parents. I also bought the ebook It's No Accident, which I found very interesting and useful. I would say that helped me the most to understand my daughter. It has some very interesting ideas about the reasons for accidents and potty training problems, written by a paediatric urologist.
It's very frustrating. Good luck to you and the parents!