Southwest doesn't have that option. They can only ban passengers from their own airline.
If the FBI is involved (interfering with a crew member's duties is a federal crime), they can add her to the no fly list via TSA if warranted. And I think all of these people that act up should be, or in the case of psychiatric reasons, should be required to fly with a caretaker.
I am not sure why my other comment was downvoted to oblivion. ONE airline banning a passenger is NOT the same as being added to the no fly list. Period.