Re: Shenandoah National Park
I highly recommend white oak canyon. It might be too much for the young ones to do a whole loop (many steep switchbacks), but you can make an easy trip to the first and second falls and there is a primitive campsite before the trail begins coming from the road (not the at trailhead).
Park at the lot. To the left 50 yards from the lot is a great clearing for camp, and has a fire ring. To the right is the beautiful trail.
Btw. The whole trip I hung and had no problem hanging.