There's also the fact that Nolan has a son himself, so the idea of relating to that kind of father/son dynamic was easier for him and really, that's all the story essentially called for. Yeah, he could have blown it up and included more of the Gordon family, but as the man was stuck trimming fat off of the movie anyway by the time TDK had to be ready to go, it probably wouldn't have made to the screen anyway. Finally, it's probably a bit of a holdover from Year One, where Gordon's son is put in danger and Batman winds up saving his life. I guess with all the attention Barbara Gordon (Batgirl) had gotten in media over the years, focussing on James Gordon Jr. for a bit was definitely a new way to go.