The TV-show dream in this story happens at the beginning to show the reader the nature of the relationship between the narrator and her daughter, Dee. The narrator talks of the "TV shows where the child who has 'made it' is confronted, as a surprise, by her mother." This informs the audience about the nature of these types of shows. They are a chance for often estranged family members to reconcile their differences, apologize and give thanks to each other.
The fact that the narrator dreams of meeting her daughter on one of these shows tells the reader a great deal about their relationship. This shows the reader that the narrator has a very complex relationship with her daughter. It also shows that the narrator feels that her daughter has achieved success in the world but she, the mother, feels as if she has not been acknowledged in the achievement of this success. The narrator tells us what she is like "in real life", but then tells us what she is like in the dream. She is "the way my daughter would want me to be". This indicates a sense of inadequacy felt by the mother and a sense of shame felt by Dee for her mother, always wishing she was something that she was not.