i think you could probly try to explain the situation to someone, be nice, and just hope for the best. although since it involves dropping off your dog, they might not give you a break as that is not really any form of emergency/distress.

im not sure if this will work, but what if one of you drives and one of you flies on the plane, claiming that since the first plane is small, the one person that flies claims that they need to use two tickets. would this work?