Kate to george:"you dont hate us, george, i know you, you cant fool me, i diapered you". what is kate trying to achieve in this conversation with george?

Kate is trying to reestablish their history. She and Joe were close to George and Anne's parents, the children grew up together. George's visit with his own father has created hostility (namely the reason why his father went to jail). Kate uses a motherly tone in order to play upon the past, remind him of their relationship.