Instead of looking at it as something that will upset the parents think of it as a huge gift to them. They need the life experience of one adult after another saying "not on my watch". They need to hear that the child has behaviors that you won't do in your business. The next provider will tell them too. They need to hear it OVER AND OVER again. Just think of yourself as a brick in the wall of their understanding, accepting, and dealing with their child.
We sometimes have a tendency to over rate our actual impact on families. We put ourselves so highly in their life and sometimes we are. Some times we are just a stop over to teach them one thing about their child. In this family's case, your role is just to say NO. They don't need anything else from you but that NO. You don't have to offer up fixes or appologies. Just do the NO and have them go about their way.
I don't believe they can't do anything with her. My gut tells me they just don't want her to cry so they are allowing her to behave terribly so they don't have to pay when they tell her no. Time for them to be put to the test to see what they can do. They will most likely go thru a few more places before they actually get it so your terming now is just one piece. That's an important piece tho.
Hold your head high and be firm. Tell them that her behavior is not appropriate for your environment and she can't continue to attend. They won't like it but believe me, they will hear much worse in the future. A few years from now they won't even remember your name and won't give a thought to the no you are giving them now.

