What sort of clues would give them the impression that he is somewhere near the home? It seems like that would have to come from a family member or from the knowledge that certain items are missing. Perhaps they believe he grabbed guns, food, water and maybe left on an ATV or on foot. It seems unlikely to me that he would be in the area. So there has to be some solid information pointing them in that direction.
Since they are checking random vehicles, I get the impression they believe he went into the forest and is expected to pop up at a home in the area and that he may try to take a car from a home and flee the area.
It is obvious that a guy who owns guns and lives in rural Mississippi is probably a hunter. So he probably knows the area very well. And don't underestimate how rural this area is. In the popular travel book, "A Walk in the Woods," the author tells a story about a plane crashing in Maine. It crashed in the forest, and they didn't find it for years and years.
With food and water, the guy could be in the woods for days. At some point, though, he's going to need to return to civilization. This seems like an EXTREMELY volatile situation. If he is still in that area, nobody living in that area is safe. He could already be holed up in a home and could force a homeowner to tell police that things are just fine.
Of course, he also might be nowhere in the area. If he works in a garage, he probably has access to some vehicles.
If he really loves those children, I hope he realizes soon that he needs to take them to a road and leave them to be rescued. That is what a good father would do.
