Hi there. I hope this answer can serve those who will face same/similar issues in future. Sometimes what causes issues is so small, experts wouldn't even bother looking at it...
TL : DR
Make sure your coolant level is 'as advised' and not 'more'.
The longer version
I ended up here because I recently ran into the same issue: strong wobbling while accelerating (almost at any speed), smooth drive while non-accelerating. Could not find any answer though. In my case I figured out the issue myself.
The night before I saw an error message (B200) asking to top up coolant. So I bought some coolant, mixed it with distilled water and made the refill. Am no car expert, but looked up a few YouTube videos on coolant top-up procedures (no disrespect to the experts in the house). While filling the coolant, I noticed that there is still so much to fill into the coolant container… so I made it full (way beyond marking). Switched on the engine, coolant warning light was no more there. I went to bed.
Next morning first thing while leaving the parking lot, I feel a severe wobbling on steering wheel and gas pedal while accelerating. when I reached office I asked some colleagues whether topping up 'too much' of coolant would do any harm or cause any side effects, they said it should not be any issue. I still had my doubts, because I felt it couldn't be coincident. I thought of siphoning the excess coolant somehow. After having done so and reaching the coolant container marking, I made my test drive... and voila! All good, no shivering, no wobbling, no nothing.
Hope this helps