How can I force the Mac app store to re-install an application?
For Xcode, try to go to /Applications and move "Install Xcode" to trash.
I think Xcode is a special case, it doesn't get deleted when you delete it form launchpad.
First, you can try to remove all remaining traces of the old program. Search your whole hard drive (including all partitions and accounts), and attached external drives for related files and remove them.
If you can't get the App Store to believe that you don't have the app anymore, hold down option and click on the Install button. That will let you download it, and the installer will probably work.