Lot's of questions. Are you using the same WDH? Is the receiver height the same? Quality of tires on the new TV? Tire air pressure? Did you go to a 4WD or from a 4WD to a 2WD? Is the TT loaded the same?
My point is something changed in the setup, you need to determine what changed and correct it.
When I left the dealer with the our new TT the ride home was scary to say the least. With the help from this forum and several adjustments to the WDH and tire pressures I finally got it right. I even installed a Bilstein steering stabilizer which made additional improvements. A set of Bilstein shocks are next.