Unfortunately.......welcome to the rubbish 7 speed dry clutch DSG gearbox as used in lower spec VW, Skoda and Audi vehicles.
Shuddering is common. The clutches overheat in stop start traffic / steep driveways etc and burn up prematurely causing the shuddering. If the car has lived its live in a busy city like Sydney then you can bet its had to have its clutches changed at least once already.
And the mechatronics (computer controlled brain which controls the gearbox) is known for playing up on these gearboxes and many of them have been replaced either under warranty or out of the owners wallet.
Lastly....please dont tell me its a 118TSI Golf with the 1.4 twincharged engine. If so, the gearbox will be the least of your worries.
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