Typically if the vehicle starts and runs the fuel pump is okay. There are times in which the pump works but doesn't have enough pressure, these times are rarer than not. There are many components in the engine management system of your car, and almost any one of these can cause a stalling condition. I would spend the money and have a shop check it out, before I start making a bunch of expensive guesses.
The Touaregs have 2 fuel pumps, V6 and V8s are slightly different setup. (Not sure about V10)
They are both located under the back seat. You will need a special 12 point 10mm tool to remove some bolts which hold the seat brackets in place so you can gain access to the pumps covers. These bolts are very tight so make sure you use the correct tool, and a breaker bar for torque. You will also need to cut out a circular hole in the carpet above each pump cover. The covers have 10mm nuts which need to be removed. You can pry the covers off with a flat screwdriver. The old pumps have quite a few hoses and wires connected to them so clean everything and mark them before removal. Do one pump at a time. There is a non-pressurized hose connecting the two pumps as well. On the V6 3.2, the driver side is the Main Pump, and the passenger side is the aux pump which is used when starting only,(and under severe loads such as acceleration) then the main pump kicks in.
The main pump usually fails as it is used 90% of the time, but it is smart to replace both pumps. This explains why it starts and runs for 10-15 seconds and then dies. You should also replace the fuel filters--which I believe are located inside the sending unit(s). There are also 2 circular seals/gaskets which go onto the body at the pump housing. Good luck!