Well, there's Child Maurice (Child 83), but it isn't a close match. The two young men are master and servant rather than brothers, and although a meeting is arranged, it is the husband who goes, and kills the man he supposes to be his wife's lover; but who is really her illegitimate son. His wife only gets to meet the severed head. Martin Carthy re-made it as Bill Norrie.

I asked about the head as it ought to be the kind of thing that would stick in the memory, but I've known people to describe certain songs very oddly, and much at variance with what actually happened in them; memory can be a capricious thing. It's probably a completely different song that was meant.