Here's a listing for the OLD MOTHER HUBBARD book printed by McKinney for sale from a German vendor:
http://www.en.zvab.com...
The cover and taped spine binding appear quite similar to that on the copy of Moon Children that I have. Jamieson-Higgins also published YANKEE MOTHER GOOSE by Benjamin F. Cobb in 1902. This same author in 1902 had a book published in Chicago that was illustrated by Marshall D. Smith. If (as seems likely) YANKEE MOTHER GOOSE was printed by McKinney, perhaps the Cobb-McKinney-Smith connection might yield useful information if it can be developed. Gardner-Whaley-Busby speculated that author had likely been put in touch with the illustrator by the printer.
According to a 1903 entry in Bookseller, volume 8, which may be found on Google books, Jamieson-Higgins introduced a number of juveniles in 1902 and failed that same season (perhaps contributing to the bankruptcy of McKinney?). Their line of copyrighted juveniles was taken over by Hurst & Co., perhaps not coincidentally the publishers of B. F. Cobb's books illustrated by Marshall D. Smith...