That is very, very astute. Really good observation I had not noticed. Don't forget: he had a shovel in the back of his truck. He might have just been in a hurry and thrown the shovel back in in order to get back and away from a terrible scene. So that he could return home, where his cousin's girlfriend could claim to have seen him carrying the baby. A story I have never believed for a hot second.
Sorry to quote my own post...but ... this really points to a giant lie, because if he was just 'driving the baby around because it was fussy' (which we already know is a lie because the people in the store said the baby was sleeping), why would he need to stop somewhere and put the tailgate down?? I can't think of any reason.