ds1 was exactly the same as this. used to beg for a nappy when he needed to poo. eventually one day it all just clicked- he needed a poo and he went to the toilet. it really was a matter of time and patience.
our kinder will take kids in nappies but they will call you to come and change it if they soil it. how many hours is she there for?
fwiw my ds2 is 3 yrs and 10 months and is not TTed. not even for wees.