I live in Eretz Yisroel and keep one day Yom Tov. I will be at my family for Pesach in the US. How shall I act toward the second day Yom Tov? Havdalah? Tefilla? Tefillin? Melacha in public? Second seder? etc. Thanks

You keep only one day. That means you do Havdalah after the first day Yom Tov, daven the weekday Amidah and on eighth day Pesach you put on Tefilin. This however does not allow you do any Melacha on second day Yom Tov not in private and how much more so in public. This ruling is based on the concept learnt in the Talmud [Psachim 52a] that a person who travels to a place where certain stringencies are practiced, follows them to the same extent. That which is not a Melacha can be done even if is prohibited by the Chutz Laaretz people as long it is done in private. For instance – you cannot drive, turn on lights, go on the computer etc. but can have a worm shower [even if you hold the opinion you can’t have one on Yom Tov] or cook for the next day [using an existing fire]. Chametz shouldn’t be eaten till the end of the eighth day [Aruch Hashulchan]. This all applies only if you are in a city with Jews, if however you stay in a city with no Jews you can act just like in Eretz Yisrael by all means [Shulchan Aruch OC 468:4, Mishna Brura ibid, SA OC 496:3, MB ibid, see also Taz ibid and Tchumin 10 p. 369]