Dear Jon,
Very grateful for the tune to "Sleepy Peedie Laddie," which I can hardly wait to decipher. Still think I've heard it before, and that, although you are quite correct that the lyrics can be made to work for a parent of either gender, that when I heard it, it was sung by a man. Maybe the tune will sharpen my recollection. Still think it just about the dearest lullabye I've ever encountered, -- and, as the singing parent to a passle o' youn'uns I've made note of quite a few.
As part of an important chapter of American history, The Handcart Song's not too shabby, either! Might as well try 'em both.
Happy dreams and gentle rest,
Shula