unstable output MPX53

Several problems.
You supply the sensor from a (resonably) stable 3.3volt.
And probably measure with an potentially unstable Aref (5volt).
Better to power and measure from the same source.
Google "ratiometric".

The output of the INA121 could swing from ~0.15volt to ~11.1volt on a 12volt supply.
The Arduino shouldn't see more than 5volt on the analogue input. You could fry the pin.
You need a voltage divider on the output of the INA to bring ~11volt down to ~5volt.

In the end it would be easier to dump the sensor,
and buy one with inbuild instrumentation amp and temp compensation.
Look through the extensive list of amplified MPX sensors.
Leo..