Yes, you will definately be able to still swim in September. The weather doesn't start to really cool off till October or November. Also, the crowds will be considerably smaller in September...it's one of the best times to visit.
As far as the packing goes, be sure to bring sunscreen (you will still need it)...however, due to TSA regulations, if you plan to carry it on the plane, it will have to be in 3 ounce bottles or less, all of which have to fit inside a quart sized plastic bag. Just a heads up.
As for the kids...hmmmmm...I don't have kids, but when I WAS one (hahaha), I always enjoyed reading or learning about where I was going. Maybe you could bring along, for the plane ride, a coloring book or some kind of book for the kiddos? If you need a good book title about WDW, just send me a quick private message and I would be more than happy to suggest one! Hope at least part of this helped you in your planning! HAVE FUN!!!