I am searching for a book for my Uncle Frank who was born in 1929. It may be called the Witch of Windy Hill and it may be a collection of stories. In one story, there were these lines “Mrs. Mite and Mrs. Midge…underneath the wishing bridge…how I wonder when and whether she will lose her bonnet feather what a broom twood make” and there was mention of Colonel Sand, I think.
you’re thinking of “The Ghost of Windy Hill” by Clyde Robert Bulla, pub. 1968, though that might be too late for the book your uncle read. The book covers the adventures of the two Carver children in a New England country house in the 1850s, where they deal with ghostly incidents in their home, a lonely crippled boy and his cruel father, and several neighborhood secrets. There is a Miss Miggy, a friendly local eccentric, who befriends the children. It’s a good read, just a bit scary in the right way.
Basically this is a recall of the “Windy HIll”, but I don’t recall the verses you mention, they may be part of another book that’s similar. Hope this helps.