Dee is motivated by her desire to climb higher on the social ladder. She sees the old items at home that used to be embarrassing to her now as items to "display" in her urbane and up-to-date decorations in her new place. She is aggressive and tries to push both her mother and Maggie around so that she can get what she wants out of them. She sees her heritage in terms of material possessions and changing her name for more attention.
Maggie on the other hand is extremely shy and easily pushed around by her sister. Her scars created an even more reclusive character over time. She sees the items that Dee wants as useful items, not things to show off to friends. She lives the life of poverty with her mother and knows that she has to work for what she has. Those quilts were promised to her and she will one day need them/use them for practical reasons. Taking the quilts with her one day, she sees her heritage as something that is passed down from her mother to her, and eventually to her children. It would never be something she'd put "on display" like art. She and her sister never had anything in common, nor will they. Their contrasting characteristics are what create the friction in this story.