Oedipus Rex: How does familial conflict reveal the protagonist's character?

Oedipus Rex is an interesting take on family, because Oedipus is constantly ignorant of who his blood relatives are. Baby Oedipus is left for dead by his parents in order to avoid a terrifying prophecy. Thus, Oedipus grows up with the royal family of a neighboring kingdom, and believes them to be his real parents. Little to no conflict arises within this happy unit, until Oedipus is told that he will kill his father and marry his mother. In order to save his family, Oedipus leaves the city. Here, we see that Oedipus is unselfish; he is willing to desert his title and his home for the sake of his parents, whom he loves. He also places a large amount of trust in his parents-- when a drunk man tells him he's adopted, they are insulted and reassure him that he is their son. When he finds out that he endangers them, he sets out immediately.

At a crossroads, Oedipus encounters a man who will not yield to him and even tries to force him off the road. They fight, and Oedipus ends up killing the man and his companions. Unknowingly, Oedipus has just killed his own father, proving that though he is loyal, he is temperamental and unbalanced as well. Rather than respectfully deferring to the man, he insists upon battling, and shows his violent side. Upon arriving in Thebes, Oedipus proceeds to marry the conveniently widowed queen, Jocasta, and have children with her. However, the prophecy soon asserts itself in the form of a plague on the city, and Oedipus' misdeeds are revealed to him with dramatic aplomb. Jocasta runs into the palace and kills herself, prompting Oedipus to stab out his own eyes with the pins from her dress. This action is certainly in response to his own transgressions, but also a testament to the fact that he loved Jocasta, even if he loved her in a wife-sense instead of a mother-sense. His grief over her suicide is a cruel consequence of the prophecy taking everything from Oedipus; we then can see his character to be well-intentioned and pure, but grievously disfigured by a cruel fate.