Plot Idea 3
Tony spends time with Carrie for Father's day, since she grew up without a father and he grew up feeling unloved by his father, he figured it was the perfect time to fill that role.
They do some regular father/daughter activities that Carrie never experienced since she was the one without a father in her life at all unlike him. He's not the best at it but he tries his best to make sure that he's a great father figure to her, better than his own father.