Is there any rabbinical authority that allows Israeli citiizens to travel in Chutz Laaretz on second day chag?
A person living in Israel is only obligated to observe Yom Tov Sheini in Chutz Laaretz when he is in a town where Jews reside. Thus, it would be permitted to travel from one airport to another, provided the airport is out of town, but it would not be permitted to travel from within the town (with a car, etc.).
Sources: See Pesachim 52a; Shulchan Aruch, Orach Chaim 496:3;