What we can clearly see happening is that, now that Baba and Amir are in America, it is Baba who becomes more dependent on Amir and is confused by the rules of society in America. Before, it was the other way round, with Baba clearly showing himself to be strong and confident in his home environment. However, now, he is made weaker and diminished as a character in this new world. Note what Amir tells us about him:
I glanced at him across the table, his nails chipped and black with engine oil, his knuckles scraped, the smells of the gas station--dust, sweat, and gasoline--on his clothes. Baba was like the widower who remarries but can't let go of his dead wife. He missed the sugarcane fields of Jalalabad and the gardens of Paghman. He missed people milling in and out of his house, missed walking down the bustling aisles of Shor Bazaar and greeting people who knew him and his father, knw his grandfather, people who shared ancestors with him, whose pasts intertwined with his.
Of course, for Amir, what he loves about America, and perhaps why he is so successful in his new home, is precisely the way that he is able to "bury memories" here and start again. It is this that makes him become more and more responsible for his father as Baba struggles to adjust to the new reality of life in America, and increasingly looks to his son for guidance and support to negoitate their way through their new environment.
Baba and Amir's relationship changed in California, it's because they had a new life and Baba was a poor man there the exact opposite from the man he was in Afghanistan, It changed because they learned the earn each others trust and they bonded, and Amire stood up for his decision in being a writer and Baba finally respected that. Baba was this rich well-known guy in Afghanistan he was every body's sanctuary they returned to him when ever they needed help, but in USA it all change he was nothing but w foreigner who worked at a gas station, and that's when Amir knew he doesn't have to follow his father's step in business and do what he love which is writing.