Dramatic irony is present in the story. Dee was glad her first house burnt down to the ground and as her mother said in reference to the new house, "No doubt when Dee sees it she will want to tear it down." Dee has never wanted to be part of her cultural heritage and left to get away from all the memories of her home, poverty, family, etc. All of a sudden she returns to grab things that are part of her family only so she can display them to her Black Muslim family that are only interested in what they stand for and not for whom they stand for. Then as quickly as she pays a visit to the past, she picks up and walks out on "IT" again. It is obvious, to her heritage is for show not for living.
Source: The Language of Literature Book by McDougal Littell
Verbal irony occurs when a character says one thing but means another. Dramatic irony occurs when the reader knows something that a character doesn't know. Irony of circumstance, or situational irony, occurs when a character or reader expects one thing to happen, but something else happens.
Dramatic irony occurs in this story because the reader understands how superficial Dee's efforts are to appreciate her heritage. She doesn't understand the true value of the things she wants to take to decorate her apartment. Dee sees them as folk art, while her mother and Maggie still use them to live.
I believe there is also irony of circumstance as well. Dee expects to be able to waltz into her mother's house and take what she wants. Instead, the mother finally realizes that Maggie deserves the quilts because she understands her heritage. The mother finally understands her daughters and decides to give the quilts to Maggie.