Cheftaz you said,
“Since if she refuses to use beis din when she is halachicly required to for money and custody issues, beis din in turn will not be at her service in getting a “get” for her.”
You make it sound like B”D is some sort of free service offered to people in the community. B”D charges a nice amount of money (on par with what most Lawers charge) by the hour, for evrey document they write and evrey action they take. That is without a Toen a Toen will cost usally an additional 250-300 an hour.
So one is asking for any services, if I made 250 an hour I would be very happy