Billysugger:
And power the sensor from same Vcc?
Yes. The very best solution it to create an analogue supple, AVcc. Connect this to Vcc with a resistor (33ohm will probably do), and put a 10uF capacitor from AVcc to Gnd, and a 100nF capacitor across the sensor supply. Power the sensor from AVcc. Power the DAC from the 5V Vcc from the Arduino (also with a 100nF capacitor across its supply), but connect the Vref pin to AVcc. This will give you a good, stable analogue supply with noise from the digital circuitry largely filtered out.
When you fire it up and read the ADC value, you should get half-range with no pressure differential (a value of about 2048). Whatever this value is, store it as an offseet then subtract it from future readings, with the result stored as a signed integer. Now you should get zero with equal pressure, positive increasing values as the pressure at port P1 exceeds P2, and negative values as P1 pressure falls below P2. The scale should be 1.2Pa per increment, but you can calibrate it with a water column. Be careful to make sure water never enters the sensor, only air at the pressure you want to measure.
Let us know how you get on.
The idea to add extra filtering of the Avcc pin for the AVR chip is a good one and is even seen in most AVR datasheets by adding an inductor. However your idea of then wiring the Avcc pin to the Vref pin is both redundant and a bear trap waiting if one ever changes the ADC reference to the internal 1.1 (and/or 2.5 on mega boards) as high current will flow through the Aref pin causing possible pin damage. As the default reference for the arduino analogRead() function is the Avcc pin's voltage there is nothing to be gained by wiring this voltage also to the Aref pin. A simple .1ufd cap from Aref pin to ground is all that one should need to do to the Aref pin for standard analogRead() default operation.