I had a very similar problem on my Corolla one time. I'd be driving in a neighborhood situation, like 15 mph, and when making turn I'd slow down then speed back up again and the Corolla would jerk like crazy. It wasn't able to just gradually speed back up, Or gradually slow down. Sort of came on gradually but eventually got to the point it was almost undrivable in neighborhood driving. Only occurred at low speeds, in the 5-25 mph range.
As it turned out I had an emissions test upcoming so to prepare for that I changed the spark plugs, distributor cap, wires, ignition rotor, checked the valve clearances, set the timing and idle rpm. All that seemed to help the jerking problem, but didn't solve it. As the final part of my emissions test prep I used some fuel injector cleaner. Voila, that completely solved the jerking problem. Apparently the injectors were a little clogged and therefore unable to meter out small doses of fuel accurately. Worth a try anyway.
I'll add that problems with the throttle position sensor should be considered too.