How does doing the right thing not, necessarily, lead to happiness in the play?
By the end of the play, Antigone's views on "doing the right thing" have been proven correct and Creon's view has been proven wrong.
By doing the right thing for her brother, Polyneices, Antigone sacrifices her life, because she is put to death by King Creon. His behavior is not driven by what is right or morality, it is driven by a need to be obeyed. He must be all powerful and once he decides that Polyneices should be considered an enemy of the state, and that he does not deserve to be properly buried, he breaks a principle of their shared religion.
Antigone's desire to bury her brother is not driven by any self-interest, she wants her brother to be received by the gods as he should be according to her beliefs.
When, in the end, Creon's views are proven wrong, Antigone is already dead, but she died knowing that she did what was right for her dead brother, this was what made her happy. Although Antigone's happiness is short-lived, she dies knowing that her decision has put her brother right with the gods and that she too has preserved her faith by her actions.
People who sacrifice themselves for a cause, sacrifice the typical happiness on earth for a greater happiness in the hereafter or eternity.
thanks pmiranda--yes, Creon is wrong for most of the play--he's the tragic hero, whose in his hubris, his overweening pride, encroaches on the gods realm-- he elevates himself above their law. Similarly, Oedipus encroaches with "Your birds-- / what good were they? or the gods, for the matter that? / But I came by, / Oedipus, the simple man, who knows nothing-- / I thought it out for myself, no birds helped me," and the play single action dramatizes his being put back in his place--the gods show his his moral limits--and Oedipus feels great misery and he suffers but now that he recognizes his identity, he knows himself and only in that knowledge can he be happy.
In Antigone, Creon encroaches with "the gods? / Intolerable! The gods favor this corpse? Why? How had he served them? / Tried to loot their temples . . . / Is it your senile opinion that the gods love to honor bad men? / A pious thought!" Creon raises his proclamation, his view of the law above the gods' law, and for the rest of he play, the dramatic action brings him in line with the fundamental law of the gods--"Nothing too much." The artistic expression of the tragic hero's fall is an absolute good that celebrates a universal order--Necessity always rights man's place beneath the gods.
So when the play brings Creon in line--when he tragic falls in line--with the moral order of the universe, Creon feels bad, of course, but happiness is that he knows his limits.
The tragic hero, in this case Creon, acts out of pride. Inevitability is part of the process. The struggle against fate.
This leads to catharsis--for the audience and for the tragic hero.
Creon grows more as a character for this discovery. Antigone has already decided her fate at the beginning of the play.
Further, with the loss of the rest of his family, Creon suffers more in the end.
Right, but happiness is falling in line with the oracles, "Know thyself, " and "Nothing too much"--in Creon's moral drama, Creon falls in line mostly with "Nothing too much," with the good of moderation--(mostly).
So even though Creon suffers, he's in line with the divine order, so he's happy.
Please don't confuse the philosophical idea of happiness with a subjective interpretation of feeling/emotion.