Anyway, my car has got a rough cold start. For the first 2-3 minutes each morning it judders down the road as i accelerate....
That part sounds like blow-by around the piston rings...once the engine is warmer...the rings seal better.
This happens on my RX-7 (totally different engine..but same concept). When I get on it when its just started...it feels like its missing..and its because the apex seals (piston rings on a standard engine) arent fully against the inside of the housing...so you dont get full compression.
Just a shot in the dark?
BTW..you didnt tell us what kind of car it is.