Simple way, you could use a paid product, Recast Kiosk Manager..
Free way...
You can probably do this with GPO, but I just tested on one machine to confirm
Configure a Proxy Service for Internet, I set it to 127.0.0.1
This broke all websites
In Advanced, I then added www.microsoft.com; garytown.com. I was then able to get to any pages on microsoft's website, or garytown.com, everything else came back with proxy error.
You can also then have GPO set your default webpage.
You can create a scheduled task that runs that would close the browser and reopen it. Test out the trigger "idle", or on workstation lock.
Good luck.