If Volkswagen fitted the EGR to your car when they built it then they are responsible for it so you need to sue the offending dealer who made you pay for it using Small Claims. The EGR can only be your responsibility if it was aftermarket part fitted by a non franchised workshop.That is possible because Volkswagen EA189 1.6TDI engines are notorious for failed EGRs, even at quite low mileages and particularly if a lot of that mileage is short runs. But if, as you write, the car was always service at the dealership then that dealer is wholly responsible.