Couchie is adapted from the French word coucher for "to go to bed" (like our word "couch", which you can lie down on). And around the turn of the century in really gritty clubs and circuses (and for a long time after that) women who danced suggestively rolling their hips were "hootchie coutchie" dancers, or dancing the "hootchie coochie".
These women were not considered morally upright in the general public, so calling a woman a hootchie cooch was calling her a tramp, especially if dressed in a way that is meant to be provocative and showy. Hootchie mama is a variation on this term. (And could get you beat down if you call a woman that.)
That Britney Spears ain't never gonna get her kids back going into the courtroom dressed like a hoochie mama.
That daughter of yours thinks she looks cute in her short skirt and bare midriff, but to the guys at school she just looks real hootchie.
"Now folks here's the story 'bout Minnie the Moocher. She was a red hot hootchie coocher..." - Minnie the Moocher (Cab Calloway - 1930)