Did Kirk ever stop being the "bad boy", defying orders and doing what he feels is right?
Even in his old age.
Kirk of TOS and the image of the character in pop culture are two distinct things.
True. The only time in TOS that Kirk ever overtly violated a direct order was "Amok Time." In other cases, he bent the rules from time to time, but generally obeyed orders even when he hated it -- he was ready to abandon Spock and McCoy in "The Galileo Seven" because the High Commissioner gave him a direct order, and was willing to leave McCoy behind on Yonada because an admiral ordered it. True, he was flexible in his interpretation of the Prime Directive, but that was his prerogative as the commander on the scene, in a time when it was often not feasible to get direct orders from superiors and captains were expected to use their own judgment to interpret the rules. And in most of TOS, Kirk was portrayed as a disciplined career soldier.
The popular image of Kirk as a renegade and rule-breaker comes mainly from The Search for Spock
and The Voyage Home
. But again, as in "Amok Time," he only violated orders as an extraordinary measure for the sake of saving a friend and colleague. It wasn't his regular MO.
Let's keep in mind, though, that the Abramsverse Kirk was intentionally given a very different, far more troubled backstory. This Kirk actually is
the hotheaded maverick that his counterpart is only mistakenly assumed to be. They're the same at the core, with the same intrinsic leadership skills and virtues, but this Kirk's life history has led him to be more unruly, brash, and undisciplined. So they shouldn't be treated as identical characters.