How do you transport a patient with a broken hip across the country?

Not easitly. Transporting a patient with a broken hip across the country is a challenging and risky idea. If there is the notion of flying the patient, you must be aware of the risk of blood clots which can be very dangerous. Recommendation would first be to investigate local orthopaedic care that may allow treatment before cross country transport.
By train, RV, plane. After a person has had his broken hip fixed, and there is little pain remaining, he can travel. He can go by any form of transportation, but he will be uncomfortable sitting for any long period. So, going by train (sleeper car) or rv will allow the person to lie down, plus get up and move around to avoid blood clots. Moving around is ok in an rv, if it is parked. It is hard to lie down in a plane.