If your iPad or iPhone does not detect headphones and output sound to the speakers even though the headphones are plugged in, or vice versa, just shutdown the device and then power on it again with the headphones still attached.
This should clear the problem, and now headphone detection should work. If it doesn’t, try restoring and reflashing the device firmware via iTunes. Or better yet, just smash the fucking thing against the wall, and get yourself a Windows tablet.