It would have been about a 4 mile walk with an elevation gain of about 1000 feet. Admittedly not easy with little kids, but they ultimately did make it 8 miles in the other direction.
I can only guess they had absolutely no idea where they actually were - but perhaps thought they knew where they were. That is the only explanation for continuing forwards on foot rather than turning back. If you're looking at the wrong place on a map, especially an inadequate map, it's easy to think you're going the right way when they are 'dead' wrong.
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.
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.