Well, the supposition in the story was that they assumed a military base would have big nasty fences patrolled by guards--as opposed to being a large patch of desert that the military blew stuff up in.
Though they were in a bad situation in any case, with hindsight, they should have headed back down to West Side Road--not that there would be much traffic at that time of year. And even tried to cross the basin to Badwater if possible.
I don't think that would have been survivable. It's about a 20 mile hike down to the valley, and that day they had a high temp of 124 degrees F in the valley. Walking 20 miles at 124 degrees with no shade with a four year old and an eleven year old does not seem survivable to me. They don't call it Death Valley for nothing.
The Geologist's cabin is about 4500 feet higher than the valley, so you'd expect the high temp to be about 100, but in the shade with adequate water (which there is at the Geologist's cabin), it's probably not life threatening.
Again, with the huge benefit of hindsight, it looks to me like there was unlimited water and at least a few days of food in the cabin, but I really have no idea how often people come by there. Some have suggested starting a smoky fire, maybe with a car tire. Another option would be to leave the family up at the cabin, and have the dad head down to the valley alone at night or very early in the morning to get help. He'd be able to move a lot faster without a four year old in tow.
Though they were in a bad situation in any case, with hindsight, they should have headed back down to West Side Road--not that there would be much traffic at that time of year. And even tried to cross the basin to Badwater if possible.