I think you may have that backwards, unless I'm misunderstanding you. If you were to look at a map of the U.S., and picture it a great big vehicle, the eastern seabord is the leading edge. Thus the earth would be rotating from west to east. The shuttle, as I understand it, would move in the same direction as the earth precisely because this gives added boost to the shuttle's speed relative to the center of the earth.
The reason for my confusion in my earlier question was that I thought the shuttle was supposed to land in California or somewhere thereabouts (Edwards Air Force Base, IIRC). I was totally unaware that Cape Canaveral had a landing facility. I thought it was launch only. Another poster corrected me.