I'm sorry but the DSG is not a true automatic. It is a Direct Shift Gearbox that is shifted by the computer controlled Mechatronic unit. Thus the DSG. The dual mass just softens the shifts and it does have 2 wet clutches in a single drum. Each clutch runs one of the 2 gear shafts. One shaft has 1,3, and 5 while the other has 2,4, and 6 on it. One shaft is shifts while the other is driving the car and when it needs the next gear it simply releases 1 clutch and engages the other. Now Tyler just hope that your dash don't go to flashing where the PRD123456 gear indicator is. If this happens you need a new Mechatronic unit. Pain to install and they don't give them away cheap but that how I got my 06 for 1200 at auction with 110k on it. Listen once you pull that trans VW makes a dual clutch kit with everything you'll need to install new clutches. A lot of the time when our dual mass flywheels go out they wobble and damage the clutch drum in the front of the DSG. If you have to pull it twice well. I did both at the same time.
VW calls it the (Torque Converter) part #02e398029c (Audi's higher torque setup for the DSG). Now if you just really want the VW version of that just use #02e398029b. Oh by the way your Mechatronic unit if it should ever go out Part #02e325025atz5w and yes that is the flywheel you need.