If for some reason you are still interested in re-marrying your spouse in New York, the marriage laws permit this, but you would be well advised to consult a private attorney or contact Lambda Legal's Help Desk before you take this step to determine if it could carry legal complications for your family.
I wonder if Lambda could be more helpful, perhaps by enumerating some of the possible "complications." The date of a marriage determines many things, including eligibility for certain benefits and accrual of marital property. The house in one spouse's name bought after the first date but before the second? It's marital property if the first date counts, but if the first date counts then what is the second date? Will someone argue (one of the spouses, even, when things turn ugly) that the first date was somehow symbolic but not legal? Assume the couple lived in New York before New York officially recognized same-sex marriages from elsewhere. It is clear the couple's marriage is now recognized, and that means it is recognized as of the date the couple married. If they marry again, one partner may later argue that the first marriage was, indeed, symbolic, some kind of political act never intended to have legal meaning, and that the later marriage in New York shows the couple intended only from that date on to be legally married.
And if years from now they divorce and mention only the New York marriage date, are they divorced? The possibilities give me a headache.
I've yet to find an LGBT family lawyer in New York who is advising her clients that it's fine to marry again. Yet all the discouraging is not dissuading those couples who really want to do this, and since the state allows it there is nothing to stop them. It's asking for trouble down the road.