I heard another version many years ago sung by Jimmie Driftwood (who wrote "The Battle of New Orleans")

He started out with a talking part about a daughter asking her father if she could marry Johnny Jones. The father sings:

Daughter oh dear daughter, you'll have to find another

You cannot marry Johnny Jones for he is your half brother

This repeats for two more boys then the daughter sings to her mother:

Mother oh dear mother my poor heart is undone

Every boy I love turns out to be my father's son

The mother replies:

Daughter oh dear daughter go on and make your vows It ain't no sin cause you ain't no kin to your pappy anyhow