I second the IR approach. Forget about the Android tablet - at least initially - and
connect an IR detector [$2 device] to an Arduino, and figure out how to use
the Arduino to pivot the TV. Can probably be done with an Arduino motor shield
and geared-down motor. You'll have to figure the mechanical attachment yourself.
Then, as mentioned, use the Arduino to pick up signals from unused buttons on
your TV remote, to pivot left-right under manual control. I'd say that building the
mechanical rotator is by far the most difficult task here.