Is it permissible to send a daughter to study medicine in Jordan, with accommodation in mixed female student housing, and traveling alone to and from, knowing that the goal is to treat women and preserve their honor in light of the lack of female doctors in their mixed village?

It is permissible for your daughter to enroll in the university in Jordan, with reservation regarding free mixing and traveling without a mahram (definition), because the harm of that is less than the harm of Jews and Christians being exposed to the private parts of Muslim women. Islamic law is built upon achieving benefits and preventing harms, preferring the better of two good things, and warding off the worse of two bad things.