Given that Hassan is a very, very intelligent man and one with a relatively wide experience at the time he returns to Kabul to live with Rahim Kahn, it makes sense for a number of reasons that he live in the small house rather than the large one.
He understands his place in the society of Afghanistan and knows that it won't be seen as proper for him to be living in his former master's house regardless of whether or not he has permission. He is comfortable and proud of the role that he plays in supporting his former master and his former master's friend and the household and he doesn't need the comforts of the big nice home to add to that.
He also likely feels comfortable there, having grown up there. The bigger house may have presented an uncomfortable circumstance for him, one he'd rather avoid.