The whole extended family has the big seder on the first night, but my parents want to host a seder too, so they've been having one on the second night for the last few years. And I think second seders can be useful for solving all kinds of dilemmas - e.g., having the seder with one side of the family each night, or having a different style of seder each night. That said, I would also be fine with one seder, since the second night has no special status.
While there are reasons that having two seders is beneficial, the second seder should perhaps ideally take place on the 7th night, when (a) it is yom tov, and (b) it is more feasible to be in an entirely different city than one is in on the first night. I have long lamented that I'll never get to have a seder with my non-Chicago friends, because we're all in our respective ancestral homes for the beginning of Pesach. But, in theory, (once I start actually kashering for Pesach rather than taking the easy way out) we could have sedarim with our families on the 1st night, and a seder in the city where we live on the 7th night. I'm not sure how well this would work in practice, because I'm not sure anyone (including me) has the energy for a seder after 6 days of this. But it's a thought.
What changes should a one-day-yom-tov person be aware of when attending a seder on the second night?
- For the first cup, I just say "borei p'ri hagafen" and don't say the rest of kiddush, since it's not the beginning of a yom tov.
- I (silently and inconspicuously) say havdalah for the end of yom tov (hamavdil bein kodesh l'chol) with whichever cup is appropriately timed. This year, the first and second cup happened while it was still light out, so this should have happened with the third or fourth cup. Except that it slipped my mind, so I did it after the seder.
- I'm ok with saying the blessing ga'al Yisrael with the second cup. We always need redemption.
- I don't say al achilat matzah or al achilat maror, since it's only a commandment on the first night.
- I don't say yom shekulo tov in birkat hamazon. (However, ya'aleh v'yavo is still said during chol hamo'ed.)
- There's no requirement about eating nothing else after the afikoman (other than the third and fourth cups), since it's not a "real" seder. So I noshed on the leftovers while we were cleaning up.
- Otherwise, everything else, from "Arise My Love" to "Chad Gadya", is pretty much the same.