I am from the same area as you, have 3 kids, and try to use 2 suitcases as well. Once you've done it a couple of times, you'll get used to it, but it's not difficult.
First, assume everything will be worn twice, at least. If the kids don't like it too bad. Their friends won't be on this vacation with them, and if you're going to the parks nobody is going to pay attention to what they're wearing.
Also make sure the items don't need ironing. Shouldn't be a problem with the kids - jeans, t-shirts, and so on.
Since you're travelling from CT (it's really warm this morning isn't it?), wear your sweatshirt on the plane. Do you really need more than one? See above - if you need the sweatshirt, nobody will care if you wear it multiple times.
As for weight, yes use the bathroom scale, but allow 5 lbs for error. Also, if you're planning to buy souvenirs, put something similar on the scale with your bagage when you weigh it (or in the bagage to ensure space as well), to avoid problems on the return trip.
We travel regularly with 3 kids and 2 suitcases and have never paid for heavy bagage. As others have suggested, since you have 5 passengers, a lightweight duffel or backpack that could be checked in an emergency is also a good idea.
For those suggesting going only with carry-ons, have you travelled recently with a family? Sure, everyone could carry their own, but you're bound to have something that won't make it through security, and will have to check something anyway.