“She did ask them. She asked them to divorce her from her husband.”
No. She asked them to facilitate the writing of a Get and that only because they are the only ones who can possibly do this. The only place you can receive a Get is in B”D.
Batei Din will even say that if she somehow gets the goyishe courts to force the husband to give a Get that the Get is no good and no one can marry the women. So it isn’t true that she has an option to go somewhere else for a Get.