She says she will sue for reimbursement for her hotel, rental car, and gasoline costs for the last leg of her trip.
Southwest claims they are obligated under FAA rules to deny boarding to any passenger "whose conduct is offensive, abusive, disorderly or violent or for clothing that is 'lewd, obscene, or patently offensive.'" An FAA spokesperson says there are no such federal rules. Historically the FAA has required airlines to operate by rules which the airlines are not allowed to publicly reveal, such as those about requiring identification that were at issue in John Gilmore's lawsuit.
If Southwest's claim about an FAA rule is correct, they had already violated it since they allowed her to board and fly half of the journey. Unless she was creating some kind of a new disturbance, putting her off half way through the flight seems pretty outrageous.