In Houston, my hometown, "whip" has been a popular term for years, since the early '90s. Not sure if it originated there or not -- but it probably has as much a claim as any big, poor, Southern town.
I've gotten the impression that it has nothing to do with a rein. I think it has to do with "whipping back and forth", as in steering. In this parlance, (fancy) wheels are known as "swingers" and cruising is known as "tipping".
I remember a pretty long thread on the (now-defunct) Swisha House message board about all this, and to make a long story short there is no definitive answer -- not even from people in the neighborhoods where these terms probably came from. Language -- and especially slang -- lives on its feet.
rs