Have you got rotation lock on (is there a lock symbol at the top of the screen next to the battery indicator) ? If so, then depending on how you've got Settings > General > Use Side Switch To set, it can either be turned off via the switch on the right-hand side of the iPad, or via the taskbar (double-click the home button, slide the taskbar to the right, and it's the icon far left). More info on the side switch/taskbar here http://support.apple.com/kb/HT4085
You stated that the side switch is set to mute. That means that the rotation lock switch is in the Recents Tray. Slide the tray to the right so that you see the entries at the extreme left. If you can confirm that the rotation is not locked and you're still seeing the problem, try a System Reset. It's easy, quick and harmless:
Hold down the on/off switch and the Home button simultaneously until you see the Apple logo. Ignore the "Slide to power off" text if it appears.
A System Reset does not remove any apps, music, movies, etc. nor does it cause any settings to revert back to default.
Also, you might wish to download the iPad-2 User Guide. Be forewarned that it does not describe the rotation lock function well.
Finally, the User Guide can be downloaded at no charge via iBooks and a less comprehensive version of the Guide is included as a Safari bookmark.