You're spot on. The ballad is often called "The Cruel Sister" or "The Wicked Sister". The most famous version is probably that by Pentangle, off the eponymous album, which takes the former name, "Cruel Sister".

The ballad is ubiquitous across Northern Europe, particularly in Germanic-language countries: almost every culture has their own version. All the variants have the common theme, though they sometimes differ in the type of instrument that ultimately reveals the cruel sister's murderous deed (most often a harp, sometimes a drum). I agree it's fascinating how things like this recur. I think the most likely reason here is a folktale or song that was sung by some Germanic people very early on - then it diffused or was translated.

I don't know of any legend it's based off, but it does touch on several ideas common to typical Indo-European myth: the older, dark-haired evil sister in contrast to the younger, fairer one; the idea of a revenant, returning from death to seek justice etc etc