I think what is important to remember about the way Scrooge acts toward his nephew is that in the beginning of the story, he is in his own world, not realizing necessarily how harshly he comes across to other people, including family members. Because of this, he acts unkindly toward his nephew.
Throughout A Christmas Carol, however, Scrooge is visited by a series of spirits: Christmases past, present and future. These spirits show him how his actions have affected him and the people around him, and how they will continue to affect those people. What particularly pains Scrooge and prompts a turn around is when he sees his nephew in Christmases present and future not speaking kindly of him with his friends, and not remembering him fondly in the future. He decides at this point that he wants his family to remember him fondly, and this includes acting much more kindly toward his nephew.
At the outset of the story, Scrooge exhibits a less-than-caring attitude toward his nephew. The nephew wants him to come to Christmas dinner, and extends his hospitality to Scrooge. However, his uncle rejects the invite on the premise that Christmas and all related activities are "humbug."
As the story progresses, Scrooge undergoes a change of heart toward Christmas in general, and toward his nephew. By story's end, he makes the decision to join his nephew's family for Christmas dinner, in dire contrast to his previous thoughts about the holidays.