That was the cutty stool or stool of repentance. Your gran's 'cuddie' was perhaps the same word, though it's worth noting that a cuddie is sometimes a donkey or (perhaps by extension) a simpleton; do you remember which meaning was intended, or was it never mentioned?

It's likely enough that the various 'stool' customs relate to one another; perhaps 'pirie's chair' was originally just a small chair of the sort mentioned above. The association with hell goes back a couple of centuries, at any rate: Motherwell ( Minstrelsy, Ancient and Modern, 1827, lxxx-lxxxi, note) quotes the verse later included in Child, adding:

"The Scottish Parliament seems often to have afflicted itself in passing acts against the sumptuous and costly claithing of ladies. But this ballad must have done more good than a hundred sumptuary enactments, for it consigned the fair contraveners at once to hell, and to a particular spot of it, of which my ignorance of localities does not enable me to give any farther information than the text affords."