It is possible but would be ugly in the long run without a custom built rom (http://xda-developers.com has instructions on how to do this), I wouldn't know where to start code wise - but there are a couple of applications which portray this kind of functionality - TodlerLock is one such app - its designed to stop todlers from from doing anything on the device, whilst the application keeps them entertained. It appears to intercept all button presses and acts as a home application to do this for the home button.
Then there are the programs like estrongs security manager that allows a user to set a password for some or all applications and basically stops the application being run without the password (it appears to intercept the intents and opens the security manager requesting the password first, if it fails it finishes the intent) - this maybe a much easier option to use something like this - you could set a password for most things, including settings and the security application itself, everything bar your application. This will stop the user doing anything you dont want them doing without the password.
You would have to set up the device for the user before hand though, as any home screen intercepter application can be changed but the user - so you would have to set the default, then lock access to the settings so the user can't change this action.