Earlier in the story, Amir also feels that he has to choose between his father, Baba, and his servant/friend, Hassan. Amir's jealousy of his father's affection toward Hassan led him to sabotage the family unity by planting a watch and money under Hassan's mattress. Expecting Hassan to be punished for stealing, Amir assumes that Baba will expel him from the household, leaving him alone as the receiver of his father's love. However, his plan backfires somewhat when Baba forgives Hassan instead. Ali and Hassan leave the house in disgrace, but Amir comes to realize that his deed did nothing but leave him with a lifetime of guilt.
I am not sure where this came from but if I were to think hat he had to choose between two people I would have to say it was between his life in America with his wife and Hassan's son, Sorhab. When Amir is asked to go after the boy and find him he thought about his life in America and how could he put himself in danger to bring the boy back to safety. He was not even thinking about taking him home with him.
Later Amir came to realize just how much he was risking trying and saving Sorhab. Once he had him he could not leave the country without getting a Visa allowing the boy into America. When he boy thought that Amir would leave him he tried to kill himself.
It could be either:
1.) Baba and Hassan -> Amir chose to win baba over with the kite than rather save his friend
2.)His wife and Sorhab -> Leaving his country was very dangerous because his life might not have come back from then and he would have then lost his wife, but he rather chose to redeem himself.