Being a Grannie of 2 Scottish grandchildren who regularly sing this in school, I love it, including the line mentioned by Guest in 2010,
"Aye, yi yippie, grannie is a hippie". I think it was either Hamish Imlach or Billy Connolly who put that line in.
I would usually sing "faither's mammy" rather than "daddy's mammy" in the second verse.
And there are some ruder verses that we maybe don't sing with the kids, e.g.
She's got a lovely naval uniform,
She's git a lovely naval uniform,
She's got a lovely navel, got a lovely navel,
Got a lovely naval uniform.
(Deliberate double spelling to indicate double entendres!)