Old Joe as given above from English broadsides was written by Frank. M. Brower in 1844. It has 7 stanzas but doesn't have the chorus of 'Somebody in de kitchen wid Dinah' which was a separate song. The original chorus was:

Old Joe (instrumental)
Old Joe (repeat instrumental)

Old Joe kickin up behind an before,
An de young gall kicken up behind ole Jo (long instrumental)

There appears to be no evidence presented to conclusively say that there is any hidden meaning in either song. The banjo was the prime instrument of the Minstrel troupes. It is at least 50% certain that the song is literally simple and straightforward.