Simple question, complex problem.

First, by "the melody" do you mean 1)the sequence of notes that Ricky and Emmylou think of as the melody or 2)the sequence of notes which the author intended to be the melody. The two can be quite different.

As for 1, with singers of the caliber of Ricky and Emmylou it can sometimes be literally impossible to figure out what they are singing as the melody simply by listening to their version of the song. There are some loose "rules" for the sort of harmony they are singing, but singers at their level don't follow them slavishly and they like to play around. They'll swap verse and harmony within the same verse, maybe the same line. It can often be helpful to try to figure out what their source is and go listen to it. Sometimes it can help to listen to different versions of the song by different people to get a "feel" for the song and the possibilities for variation. Unfortunately (fortunately?) when a song enters the tradition it is not unusual to have several significantly different but equally "valid" versions develop.

As for 2, try to find the original written/published source. If you cannot find that, try to find someone who claims to be doing the original version.