"higgledy-piggledy"

When I was small, an aunt used cross her knees, and have me sit astride her upper foot while holding my hands, and sing
a nursery rhyme:
This is the way the lady rides, prim, prim, prim.
This is the way the gentleman rides, trim,trim, trim.
And this is the way the farmer rides, hobbledy gobbledy,
hobbledy gobbledy, gee! ( The last part being a ride very much more violent and erratic.)
I have read the term "dandle" used to describe giving a very small child such a ride.