Ironically, the resolution to this conflict is unlike anything else the narrator obviously did (or did not do) in Dee and Maggie's lives. Looking at Dee's personality versus her sister Maggie's, it would be appropriate to assume Dee was very rarely told "no." She is ambitious. She does what she wants. She even has the audacity to change her name and announce this new identity to the very woman who gave her a name in the first place.
The conflict with the quilts is resolved quickly and relatively cleanly. It starts with Mrs. Johnson's remark: "The truth is...I promised to give them quilts to Maggie, for when she marries John Thomas." Despite the miniature temper tantrum the ensues from Dee for the next couple lines, this initial response shows the narrator's mind is already made up. She allows Dee to throw a little fit. She then allows Maggie to cave to her older sister and say that Dee can have the quilts. But without another word, Mrs. Johnson finalizes the fight with:
I did something I had never done before: I hugged Maggie to me, then dragged her on into the room, snatched the quilts out of Miss Wangero's hands and dumped them into Maggie's lap.
The narrator, for the first time (perhaps ever) chooses Maggie over Dee. The impact is so profound for both that Maggie is speechless and Dee immediately leaves.