Nick at his core is a coward. He's a below average, disempowered man who had to lock up a teenage girl in order to feel powerful. Everything he does displays his innate cowardice and Nick's behavior during the escape is in complete alignment with his psychology.
Nick wants to believe he is a good man. In his mind he takes care of Joy and Jack, he provides for them, he buys Jack a present for his birthday. He doesn't want to believe he is a bad guy. So if he has to face his dead son wrapped in a rug because he wouldn't take him to a hospital, that whole story in his head falls apart. He becomes a villain. He can't face his guilt, and that has him put the rug in the truck without checking that his son is actually dead.
And even if Nick did just throw the kid in the truck under what circumstance would he leave the kid on the road after a bit of a struggle? That kid would be put in the truck, the observer would think it was just a kid having a tantrum, and never thought about it again.
Nick is a coward and he doesn't want to get caught which is why he runs away when the passerby gets suspicious. If he'd thrown Jack back in the truck that passerby could call the cops, has seen his truck, maybe would get his license plate number, has seen Nick's face, and Nick could go to jail. Nick weighs his options, believes the jig is up, and cuts tail and runs for it. He doesn't go back for Joy, he just runs. It makes total sense given Nick's psychology.
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