Saiello, your reasoning is sound and your circuit is sound except the -9V regulator needs a minus power supply input, say for example, as from a second 12V battery with its + terminal connected to the - terminal of the first battery. A few comments:
1. I know of no single supply amps that go completely down to zero volts, but at best only within several millivolts of it. So, if you want to go with a single supply amp, be willing to sacrifice some PSI at the lowest end. You don't have that issue with +/- supplies.
2. Personally, I would go with an amp designed for your purpose, say an AD623 for example. There are many others. It has built-in matched resistors and a single resistor for gain programming. This way you can adjust the gain based on all the extenal components, without matching/changing all four resistors. Some amps even have a built-in precision reference voltage use you can divide to get 1 volts for your offset. Linear Technologies makes amps with built-in references designed as your schematic shows, but with various values of matched resistors inside which can be connected in various combinations to get various gains. Still, with single supply, these do not go done all the way to zero volts. Nonetheless, your circuit should give good results, if not the most precise.
3. Your method of producing the 1V offset should include a capacitor, say 1uf to filter any noise, since noise there will show up on the output amplified by two. With a battery power supply this is less of a concern, but still good practice.
4. The sensor output resistance and the output resistance of the 1 volt source should be matched for best common-mode noise/voltage rejection. Those resistances would be added to each of the 100K input resistors when calculating the gain. With a difference amp you can get the correct gain alright, but I would still make the attempt to match those resistance, or buffer them to produce a nill output resistance. The AD623 has such buffers built-in, thus forming a improved version of the difference amp with three amps, known and an "instrumentation amplifier".
5. I would think that the sensor might need a regulated voltage source to drive it, also. It depends on the sensor. The sensor's output resistance may vary with pressure for all I know, which would pretty much require a buffer amp after it, or the gain of the circuit will change with pressure. A buffer amp may be built-in to the sensor. I don't know.
A lot depends on how much accuracy you want. If you are looking to get pretty well into the ball park than just build what you have in your schematic with a good, precision op amp and 1% resistors.