The phrase was first coined by James Joyce in his smash-hit musical, Annie, in which he geniously depicts the stereotypical Irish-male's concern for slamming whiskey and disrespecting women, especially the ones from the loins of his sinner wife. (See child support.) Several years later, Joyce also uses this phrase in a letter to his actual wife to describe his penis.
1) Beat that thing like a red headed stepchild.
2) Perhaps I can help you beat your red headed stepchild. With my mouth.