Toilet training is such a difficult thing and it is so different for every child! I have so many questions going through my head.....
What kind of method are the parents using at home? Are they actually bringing her every hour without her asking? It is so important for consistency between home and daycare, although the child's reaction to it could be different.
Is there older kids in your care that are toilet trained? If so, using them to encourage her and always identifying when x asked and is going to the bathroom.
I always use cheers and songs as well as dancing when they go or sit. And try to progess this to them acknowledging they have to go and them with them asking.
Does she seem to know or care when she has an accident in her pull-up?
How long has this type of training been going on? Are the parents open to trying other methods at home because once pullups are thought as another type of diaper they are not a training tool anymore?

As for your toilet training policy.... I find that the part about being responsible for paying for damages is really scary! As a parent I don't think I would want to sign that. I think it is our responsibility as providers to determine when the child is ready to wear underwear in our care and we then accept the possibility for accidents (as they unfortunately sometimes happen). If the child is not ready to be in underwear and come to daycare dressed inapropriately, they should simply be refused at the door. We work hard enough and do not need to be cleaning messes when a child is simply not ready.
I wish you luck with this... continue to be patient, have a good discussion with the parents and go from there!