MKIV GOLF GT TDI Engine shake problem NEED HELP please!!

[MKIVGolf130]

i am writing to you to ask if you would be able to actually pinpoint what is causing my whole engine to shake when i turn the engine on (when the revs are idle, either moving or stationary, and when i accelerate in all gears at any speed, up to 70mph (obviously)) but the thing is that it picks and chooses when it wants to play up and today was the worst its been but when the Mrs drove to work it was perfectly fine,
2 different mechanics have mentioned it could be the flywheel but have also heard it could be the engine mount, i have noticed that (what i think is) the inter cooler is sitting below the front bumper by approx 2 inches and wondered if that is normal

I also had a look under the engine while the car was running and noticed that the furthest back cog that the belt intertwines around on the drivers lower side of the engine looks like its spins of axis (kinda like a buckle)

either way this is ruining my driving experience and engine power as when i accelerate i have no oomph, no back of the seat pulling when i take off from a junction/roundabout/traffic light

VW
Golf
MKIV
GT
1.9 TDI
130BHP

Can anybody please advise me please and also tell me if i have to have a mechanic do it or is it possible for a competent person to tackle

[Crasher]

Yes it could be the DMF but also on a car of that age, many other issues such as injectors or their wiring harness, you make no mention of a code read. The intercooler should not hang below the spoiler and the pulley you mention will be the one for the air conditioning which only engages (electro magnetically) when required