Factual error: It would be virtually impossible to get from Atlanta, GA to Thule (Qaanaaq) Greenland in the time-span presented by the movie. The distance from Atlanta, GA to Ottawa, Ontario is approximately (direct) 1,200 miles which would take about 17 hours of driving, not counting breaks and side trips. The distance from Ottawa to Thule is approximately 2,200 miles. Plane type? Taking a guess, range of about 900 miles. Even with no fuel limitation, flying time approx 10 hours.
Answer: It's entirely possible. Rapunzel has a similar face appearance to her mother's, and you could also count the family bond of simply knowing. She also has green eyes, which are uncommon, so the parents probably knew that she was unlikely an impostor.
virtual-toast