Second all Blinkers has said.
Having tubed many small species ( sorry not farm animals,just dogs, cats, rabbits etc ) I would say it is almost impossible to get the tube into the airway without the animal fighting and coughing as you block the airway. If she didnt cough and gasp for air it would have been in the stomach. It was most likely an internal problem causing a reflux of the milk which subsequently got inhaled after syringing, in which case it would have happened even when she suckled from mum. It sounds to me like there was an irreversible problem.
Whatever the reason for her loss, you did all you could to the best ability. Nobody is to blame at all. She had the bestlove and care anyone could wish for in her short life.
