Are there any halachic authorities who permit one who lives in Israel to take a short vacation (two weeks) in chutz la’aretz?
If the vacation has to be in chutz la’aretz for reasons related to a mitzvah — for instance, to visit family, or for shalom bayis purposes, or for visiting graves of tzaddikim — then several authorities permit the vacation. If there is no purpose beyond the vacation, which can also be achieved within the Land of Israel, then no poskim permit it.
Sources: Although only three reasons are mentioned by Chazal for which it is permitted to go to chutz la’aretz (getting married, making an income, and learning Torah), poskim write that it is permitted to do so for a variety of additional mitzvos (Rambam already mentions honoring parents, which is not mentioned by Chazal). This is the reason for which we find many prominent rabbis going to chutz la’aretz, even for the purpose of a holiday, because they feel that this is necessary for their health, or for visiting graves of tzaddikim (some do not consider this a mitzvah), and so on.
See also Chavas Binyamin (vol. 3, p. 60), and Ateres Paz (Yoreh De’ah, no. 10), who write that the prohibition of travelling outside the Land of Israel without a valid reason is because one shows that the Land of Israel is less precious and desireable than foreign lands. This would certainly apply to a holiday, unless there was some added reason that can only be achieved outside the Land of Israel.