The suggestion that The Two Brothers and Edward are successive episodes in what was previously (let's not say "originally"!) a single story reminds me of the recent discussion in the Origins: George Collins: revisited thread about about Child 42 and 85 being probably parts of a single story. It is certainly possible to construct a story starting with rivalry between the brothers over a girl (who might or might not be their sister), followed by the killing "accidentally on purpose", then the dialogue with the mother including the nuncupative* will and the list of impossible events that will precede the murderer's return to his home, and finally the girl's weeping/singing/charming the dead brother out of his grave "because that he couldn't get no rest" as one of the American versions has it.

But equally the folk seem to have been happy with having them as separate stories. You pays your money …

*A word I had not met until I read Archer Taylor's fascinating book "Edward and Sven I Rosengard†: A Study In The Dissemination Of The Ballad".

† sic, but should be Rosengård