As we have seen, if a Diaspora resident comes to visit Eretz Yisrael with no intention of making aliya, he must observe a second day of Yom Tov. This includes not performing any melakha, reciting the Yom Tov prayers, making kiddush, and having festive meals. At first glance, it would seem that he is required to pray in private, as the Sages have stated that one who visits a place that follows a certain practice should not publicly deviate from the local practice. Nevertheless, there is a general consensus among the rabbis of Eretz Yisrael that visitors may form a minyan for the Yom Tov Sheni prayer service. Thus there is no harm done to the customs of Eretz Yisrael (Avkat Rokhel §26; Kaf Ha-ḥayim 496:38).
On Shemini Atzeret, if a guest from abroad is staying with residents of Eretz Yisrael, he should not eat in the sukka, as doing so would involve blatant disregard for local practice. However, if he is in his own apartment or in a hotel, he should eat in a sukka on Shemini Atzeret.
For the sake of a mitzva or a great need, a Diaspora resident may ask a resident of Eretz Yisrael to do melakha for him on Yom Tov Sheni. It is a case of shvut di-shvut (double rabbinic prohibition) because Yom Tov Sheni itself is of rabbinic origin, and requesting one to do melakha is another prohibition on the rabbinic level. However, if there is no great need or mitzva involved, it is forbidden to ask.
As for sukka, there are those who say that a visitor from abroad should sit in a sukka on Shemini Atzeret even when he is a guest in an Israeli’s home (Or Le-Tziyon 3:23:11; Yom Tov Sheni Ke-hilkhato ch. 2, n. 48 citing R. Elyashiv and R. Wosner). Others say that he should not sit in a sukka, for two reasons: it is a dishonor to Shemini Atzeret, and it is disrespectful of the local practice (R. Yeḥiel Michel Tikochinsky, Lu’aḥ Eretz Yisrael; Minḥat Shlomo 1:19:1; Minḥat Yitzḥak 9:54). It would seem that one visiting the home of a resident of Eretz Yisrael should not sit in the sukka, whereas if he is alone or in a hotel it is preferable that he does sit in the sukka. However, if this is difficult for him, he may rely on those who are lenient. In terms of sleeping in the sukka, even in the Diaspora the custom is not to sleep in the sukka on Shemini Atzeret (MB 668:6).
. Sha’arei Teshuva 496:4 states that just as it is forbidden for a resident of the Diaspora to do melakha on Yom Tov Sheni, so too it is forbidden for him to ask a resident of Eretz Yisrael to do melakha for him, even though the latter may do melakha for himself. This is also the opinion of Pe’at Ha-shulḥan, Hilkhot Eretz Yisrael 2:15; Minḥat Yitzhak 7:34; Igrot Moshe, OḤ 4:105. In contrast, Minḥat Shlomo 1:15:3 is inclined to be lenient, in the same way that one who has accepted Shabbat early may ask one who has not done so to perform melakha for him (SA 263:17). In practice, one should be stringent concerning Yom Tov Sheni. Nevertheless, since this is a case of shvut di-shvut (keeping a second day of Yom Tov is rabbinic, and so is asking a non-Jew or Jew to do melakha), it is permitted for the sake of a mitzva or a great need.