Interestingly, I think that the conflicts between Mama and Dee are very closely linked to the theme and the major symbol of this story. I think the theme of this story has to do with our heritage and our family history and how we respond to it. We can see this theme through the main symbol of the story and how it is used.
Clearly the major symbol of this great story is to be found in the quilts that Dee so desperately wants. Consider how they are presented in the story:
Out came Wangero with two quilts. They had been pieces by Grandma Dee, and then Big Dee and me had hung them on the quilt frames on the front porch and quilted them. One was in the Lone Star pattern. The other was Walk Around the Mountain. In both of them were scraps of dresses Grandma Dee had worn fifty and more years ago. Bits and pieces of Grandpa Jarrell's paisley shirts. And one teeny faded blue piece, about the size of a penny matchbox, that was from Great Grandpa Ezra's uniform that he wore in the Civil War.
This description shows both how valuable they are to the narrator but also what a family history they include and show. It is clear that the quilts and who they belong to symbolise a far bigger issue regarding the characters of Dee and Maggie, giving the story its title. Note what Dee says when her mother declares she had promised them to Maggie:
"Maggie can't appreciate those quilts!" she said. She'd probably be backward enough to put them to everyday use."
The final decision to give Maggie the quilts is an act of love and of upbuilding of Maggie, for the narrator rejects Dee's rather pushy claim on the quilts and gives them to Maggie instead. Thus the quilts can be said to symbolise the heritage of the family, but also the love and human spirit of Ma for Maggie as she tries to build her daughter up and show her that she is affirmed and deeply cared for. Of course, it is Maggie who, unlike her sister, Dee, has not abandoned her family heritage, and thus will use the quilts in a way that is honouring to the memory of the family history that they represent.
Thus the major conflict is between Mama, who believes in her family heritage and holds on to it, allowing it to identify and define her, and Dee, who has rejected her family heritage in an attempt to embrace an African identity.