I've run across this new-to-me term several times in the past few months-- moral distress. It wasn't developed for the teaching profession, but lots of teachers are going to recognize what is being described here.
Andrew Jameton gets most of the credit for drawing the moral distress picture, looking at the world of nursing. This piece from the AMA Journal of Ethics lays out his ideas pretty succinctly and points the way to broadening them. Here's the basic definition:Moral distress, according to Andrew Jameton’s highly influential definition, occurs when a nurse knows the morally correct action to take but is constrained in some way from taking this action.