Erachet was visiting us this evening, and brought up an interesting question. Her family lives here in the United States, but a number of years ago purchased an apartment in Israel as well. They will be traveling to Israel for Sukkos (Tabernacles), but returning before Shemini Atzeres and Simchas Torah. The question is how many days of Yom Tov will they keep in each place?
For most people, this would be a simple discussion. If they live in Israel, but merely are visiting the United States, then they would keep but one day of Yom Tov for Sukkos and one for Shemini Atzeres/Simchas Torah. If it were the reverse, they would keep two days each time. Erachet's family, however, actually owns the place they will be living in, and apparently will be keeping only one day while in Israel, but two days when they come back to the United States.
Erachet questioned this, finding it really odd: How could her family essentially change status in the middle of a holiday!? How could they keep one day for one half, and two for the next? Of course, we quickly noted that this wasn't quite the case - Sukkos and Shemini Atzeres, though closely connected, are not the same holiday. The family isn't changing in the middle of a holiday; they're merely keeping each holiday according to the place they are in.
A more interesting dilemma would be if her family would go to Israel for part of Pesach (Passover). Would they only have one seder, but then not have chometz for 8 days? Can someone change status during a Yom Tov from being considered a yosheiv Eretz Yisroel (someone who lives in Israel) to someone who resides outside the land, or vice versa? I think the question is a fascinating one, however rare it might be; I'm sure* there are poskim who hold that as their primary residence is outside, they are considered outside, while others might hold that owning land in Israel places them in the status of those who live there. I'm more concerned with what the ruling would be according to this opinion they seem to be following that it depends on where they are located, since they own land in each place - could they actually change their Halachic status within the same Yom Tov?!
This is likely far more common among Sephardim who follow R' Ovadia Yosef, who (IIRC) rules that a person must go by wherever they are whether they own land or not. This means that any Sephardi who travels in or out of Israel during Pesach should have this issue, though perhaps that is different because he rules based primarily on where the person is and not based on what status they fall under.
* I vaguely recall studying this in depth in a dorm room in Chofetz Chaim in Sanhedriya Murchevet on Sukkos one year - it's fascinating to read through all the opinions and their reasonings on the subject in general, though I don't recall reading about a person who owns land both in and out of the land and is traveling between the two.