I'm glad to see this thread; this morning I fell down a rabbit hole and have been researching different versions of this tune in hopes of finding one I remember. This site
is a treasure trove but none is the way I remember my mother singing it as a lullaby.

In her version, when the word "valley" repeats, the second syllable goes up a minor third (for those who speak Solfege, from Mi to Sol). Stays on the same higher pitch for "so", then leaps down a sixth ("Ti").
In other words, in the key of C, "Valley so low" would be E-G-G-B.
(sorry for the confusing description. It's so hard to put in writing!).

I'm wondering if my version comes from my mothers' mother's home in southwestern Ohio. I've written to a few people I found who are connected to the Ohio Center for Folklore Studies, so if I learn anything I will report back.