I finally recognized the tune to which my ex-mother-in-law sang "Today is the day they give babies away with a half a pound of tea...." It's the opening theme of BLAZE AWAY. I mistakenly called it a Sousa march above, but it's really by Abe Holzmann, from 1901. Here's a midi file. I believe the same tune is also used for "I love to go swimmin' with bowlegged [or "bare-naked"] women...."