We live in NY and have an apartment in Jerusalem and intend to make Aliyah within 4-5 years. We have had the apartment for over 5 years. We spend, on average, 4-7 weeks in Israel each year. Are we permitted to observe the holidays in Israel and the U.S.in accordance with Israeli custom: 7 days Passover, 8 days Succoth/Shmini Azereth and 1 day Shevuoth?

You will have to wait till you make Aliya in order to have only one day Yom-Tov in Chutz-Laaretz.