Couple of my favorites are Lucinda William's "Sweet Old World" from Wrecking Ball and Everly Bros.' "So Sad (To Watch Good Love Go Bad)" from Last Date. She sure feels Lucinda's pain on "Sweet Old World"--what a great interpretation.
I haven't listened to Red Dirt Girl (or anything newer than that that might feature her own songs), but when I think of Emmylou, I think, thank God for terrific singers who know terrific songs when they see'em and can bring them to life in their own way. One of the "values" that emerged from the rock era that I think is not so valid, especially when applied to other genres, is that a performer isn't a first class artist if they don't come up with their own music. Artists like EH don't need to write and perform their own stuff to elevate their artistic standing. (But this is not a comment on EH's own stuff one way or the other.)