You should actually go read the bigamy laws in your state. They will almost certainly be on line somewhere; it's just a question of navigating them. Find your state's database of statues and look first under penal code, and then under something like "Crimes Against Public Morals" or "Crimes Against the Marriage Relationship".
Most bigamy laws are worded to criminalize not only multiple legal marriages, but also purporting to marry more than one person. This is why the family on that "Sister Wives" program had to move, even though there was only one legal marriage there.
Chances are you'd be running technically afoul of the law, but since Lawrence v. Texas, chances are also pretty good, so long as there are only 0 to 1 legal marriages involved, that the SCOTUS would overturn any conviction. It's just that you probably don't want to be the test case.
That's technically. In real life, no one is going to care unless you go on TV with it. There are lots of married triads, quads, and tribes.
As far as what to do on your wedding day... I'd say do whatever the three of you decide you want. It's your wedding.