If you're making a family trip out of it/your spouse won't let you come otherwise, then there are roughly 1.6 million activities in the area to occupy children, and of course they can come to the picnic. However, all activity will be adult-focused.
Most hotels/resorts include parking, as do most places in general. Saturday AM is the Lake George Triathalon, so the main road will be limited getting into and out of town from the west (but only partially, and only til about noon). We have also been warned that parking for the fireworks cruise is tight, though the boat is located in town.
Because one of us does not render on camera as mere mortals do, and the other thinks his beard is going grey.
As any good Northern NYer (Jen) can tell you, Labor Day marks the start of 9 months of winter. So while beaches and BBQs are almost certainly possible during the day, it WILL get pretty cold at night. So bring a jacket/kindling/Mola Ram fire pit or whatever it is you need to keep warm.