How do I keep my web site from going all the way back to the home page every time I hit the back arrow?

You may get this using named anchors. In flash movies, browsers are not aware
of user actions and you need to use named anchors to add the flash frames into
browser's history so when the user clicks back, the flash goes back not the
whole page containing flash movie. Look at this simple tutorial:

http://www.flashmagazine.com/html/688.htm