Here's another children's handclap rhyme that begins with that line from the Jackson 5 song, and includes a variation of the lines about mommy and daddy. But then this example adds lines from another rhyme, one which I have found recited independently, or in combination with other rhymes:

A.B.C.
It's easy as 1.2.3.
My momma takes care of me.
My father don't yell at me.

Caught you with your boyfriend.
Naughty, Naughty.
Didn't do the dishes.
Lazy, Lazy.
Ate all the candy
Greedy, greedy.
Jumped out the window.
Man, you're crazy!
-multiple sources; collected by Azizi Powell,1999; posted on Cocojams on 2/26/2006