Well, it shouldn't do that automatically, as you might just genuinely try to run FF while it's running by mistake. But a button to do kill would be nice.
Running FF a second time works actually, all it does is signal to the current running FireFox to open a new window in the same process. The 'FF is already running' message comes-up when there is a zombie FF process going that's not responding to signals to open a window (or similar). I agree with you though, killing it off automatically isn't a very good solution, but having a button to close the current FF and restart would be nice.
If you click on the button/ launch the application it should make a best effort to show you a browser window. "Restore" a minimised window, raise a hidden window, offer to restart if necessary, etc..
