Josh McCallister only appears in the first film. He is not seen in the second film, as he, Rob, Georgette, Heather, Liz, and Mickey are in Paris. Josh has no lines and is not known that well. He only appears once in the whole film, not including the deleted scene in which is family welcomed their cousins to Paris.
Josh is first seen choose and opening presents behind the tree in his parents' apartment. He is not seen again after this, nor is he seen in the second film.