Mrs. Johnson is the narrator of the story. She is the only one who speaks to the reader. So, neither Dee nor Maggie have any direct interaction with the reader. Neither sister has any intentions of proving something about themselves to the reader.
But within the context of the story, Dee certainly does try to communicate her changing personality and her new way of looking at the world to her mother and sister. Maggie communicates very little, but her shyness and subtle gestures do suggest that she is at least comfortable living the way she does.
Dee has always been determined to be successful and Mrs. Johnson opens the story daydreaming about how that might occur. Dee goes off to college and tries to share what she's learned with her mother and Maggie. When Dee comes to visit, she informs Maggie and her mother that her new name is Wangero and that she has embraced her African heritage. She wants Maggie and her mother to understand that in modern America, a woman should understand these roots and that a modern woman is more free to express herself.
Dee is a complex character (a round character). She tries to educate her mother and Maggie, but she comes across as condescending toward them. She admires parts of her American heritage but only in a shallow way. She merely wants to display the quilts which seems more like a fashion statement than a way to honor her heritage.
According to Dee/Wangero, her mother and Maggie are stuck in the past. Dee considers herself a progressive woman, something that they don't understand or refuse to understand. This story is more complex than it would appear. If Dee actually addressed the reader, she might say that her mother and sister are out of step with history. It is their responsibility to acknowledge their African heritage and modern opportunities now afforded to women. She thinks they should be modern but ancient (African heritage). Maggie and Mrs. Johnson, on the other hand, think Dee's cultural fervor is more a matter of being fashionably modern than it is an expression of progressive feminism.