If it wasn't nap time and the parents wanted to share the great outdoors with him, why leave him to go exploring shortly after arriving? He obviously wasn't playing with Ggp, so that's one of the reasons I wanted to know exactly what Deorr was doing when last seen - playing with his hot rod on the ground, climbing inside the tent...?
They hadn't just arrived, they had arrived sometime in the morning (not sure when), then they left to go to the store (not sure when) and were back supposedly by 1pm. Maybe the parents just wanted 20 minutes to themselves who knows. It definitely would be interesting to know exactly what GGF and Deorr were doing when the parents left for their walk, and what the "friend" was doing. From the parents story, when they left for their walk, whatever GGF and little Deorr were doing, they were both hanging out by the campfire.