I do believe this originally was part of a much longer (umpty thousand verses - goes on and on and on...) ballad that was a verse morality tale that started off with the children's parents dying and their uncle getting a large sum of money to look after them - he led them into the woods to die so he could keep the money, then fate catches up with him and he becomes a broken man, etc, etc, etc...

Similar to one of the fairy tales in which the boy packs his pockets with crumbs to find their way back, but the birds eat the crumbs...

I'm not at home right now, so can't do any research on my own material.