The minimalistic style of writing mirrors the nature of the world. There is essentially nothing left; there is no society, nature bursts into flames every now and then while the left over ash falls like snow, the skies remain gray and bleak while the sun hasn't been seen in ages, the majority of the population has gone insane, etc. That is all there is written BECAUSE that is all that is written, if you get my drift.
Much of the book's language reads like Waiting for Godot, the way the boy and the man repeat "okay" and "we're the good guys."
The Man and the Boy could not take everything in the shelter when they abandoned it. It could be that the reason the family took on the boy in the end was in thanks for leaving all that food behind.
The family in the end somehow survived by scavenging what the father and boy missed despite being four people and a dog? How does that work?
The dog could be used to find hidden stashes of food that humans would miss.
As suggested above in Fridge Brilliance, the family may have found the same shelter as the man and boy. In the film (I haven't read the novel, so I can't confirm if this is true there as well), the thing that gets the man and boy to leave the shelter is the sound of a dog above them, so the family may have been very close by, or even saw the man and boy leave the shelter.
Just because it's called The Road doesn't mean there is only one road.
It's implied in the book that the family isn't traveling by road at all:
If you stay you need to keep out of the road. I don't know how you made it this far.