Certainly does not sound like you've got the judder issue as that only happens when you're moving from a stop.
The engine 'bucking' when you step on it could well be due to a clogged EGR valve - start with this first as this is the cheapest and easiest (very easy DIY also).
My own personal experience however, my jazz used to buck/shake, almost as if losing power for a split second when punching the gas, this turned out to be due to a faulty crankshaft sensor.
There's no reason for the shop to pull the transmission out (and charge you a fortune) unless YOU are 100% sure that's where the problem lies - start with the other options first.