Thanks for that tip, Trish. Looks like the song is formally titled "There's a Lonely Little Shack Amongst the Pine Trees." The only place I've seen much about it online is here: https://www.sheetmusicwarehouse.co.uk/20th-century-songs-t/theres-a-lonely-little-shack-amongst-the-pine-trees/

Here's the refrain:
"There's a lonely little shack amongst the pine trees,
And a mother is waiting there,
Ev'ry morning, ev'ry night, she'll pray,
For the one she thinks is going astray.
But I'm packing my bag to-morrow,
And I'm going amongst the scent of pine,
I'll take the sunshine back, to that lonesome shack,
And that dear little mother of mine."