To Kill a Mockingbird is just as much a coming-of-age story for Jem as it is for Scout. In the instances that Atticus tells Jem to either "take your sister home," or do something other than what he is doing and Jem disobeys, a couple of things are going on.
First, Jem is asserting a sense of independence. He wants to make his own decisions. In some cases (such as the night of the mob and later the courthouse scene) he does it fully knowing Atticus will see his defiance. Other times (the "Boo Radley Game" for instance) he goes against Atticus' directions and hopes Atticus will not find out.
In addition to asserting his independence, Jem is also discovering what his role as man in the house is. He is pushing boundaries with his father because, as the oldest and the only son, he has an innate desire to feel a sense of control. There is a point in every boy's life that he must butt heads with his own father in order to establish himself as a man. He no longer wishes to be treated the same way as Scout is treated (who Jem sees as a "child" and a girl).
I would not actually consider Jem's disobedience a negative quality. In fact, I think this shows that Jem is not only very normal, but that Atticus is a great father. Jem often wants to be near his father because he respects and reveres him so much. His disobedience often comes in the form of wanting to be places where Atticus is, rather than the opposite. What a great testimony to the role modeling Atticus has already provided. His children are not growing up and rebelliously attempting to leave home, rather, they simply want to be as included in family affairs as possible.