I've checked several of the digital sheet music collections (Hist.Am.Sheets, Levy, Indiana, UCLA, Baylor, Bodleian, Nat.Lib.Australia and a couple of others) without finding it (although Williams used the first 2 lines in Gus Williams' German Band).

There are (at least) two other collected version in the Max Hunter Collection (Nos.1033 and 1077 from 1969 and 1972 respectively).

The Bodleian Library appears to hold 2 copies of a song My Mother-In-Law from London, 1877, one specifying from Ward, Lock &Co's Humorous Songs, but not composer appears to be given and there's not text available to check if it's the same song.

Sorry it's all negative.

Mick