You should be able to log back in in the other account. So close the FB app completely and then relaunch it and try again. From the home screen do the four finger swipe up or double press the home button to reveal your multi task bar. These are all the apps that you have opened at one time. Long press the app until it jiggles and a red minus sign will appear above it. Press the minus sign, this will close the app, not delete it, now press the home button to return to your screen. It's also a good idea to close all these apps, as it helps the iPad run smoothly. Now see if it works and let us know.
Sent from my iPad using iPF