A Google search tells me Lillian Mohr Fox was involved in the preparation of school songbooks for publication by Birchard and by Silver Burdett. We have most of the Silver Burdett songbooks indexed in our School Sonbook Index, but we haven't done much with Birchard (possibly because the Birchard books are not as interesting and colorful). Maybe the song will come up as we continue the indexing project.

Oh, and here (click) is information on Terry Kluytans, who operates the "kididdles.com" Website - I don't think she had anything to do with the song's origins.
-Joe-