It's a principle of mine that a proper personal library ought to be large enough to include books one has forgotten that one owns, so I am not at all put out by remembering now that I have on my shelf The Lore and Language of Schoolchildren by Iona & Peter Opie (NYR Press 2001, reprint of the OUP ed. of 1960). As many people following this discussion will know, the Opies are leading authorities on the subject.

The Opies discuss the Mother, mother rhyme on pp. 34f with note, giving a British version that begins:

Mother, mother, I feel sick,
send for the doctor, quick, quick, quick,
Doctor, doctor, shall I die?
Yes, my dear, and so shall I ...

They give a newer version collected by A. L. Lloyd in "Lilliput" (a book or journal?) which is very similar to the one I quoted from Marnie, and which mentions the lady with the alligator purse. The Opies note that this lady is "a recurrent figure in American child rhymes;" unfortunately they don't give any examples, but they refer to the book Jump Rope Rhymes (1955) by Patricia Evans, and imply that there are examples there. The Opies anticipate me in seeing this cluster of rhymes as being basically about death. I'm not sure if the wider appearance of the lady in child rhymes in America is evidence for or against the SBA connection, but if the version Lloyd cites is British (something that isn't clear from the Opies' discussion,) that would argue against it.

Jon Corelis
Story: Parable