Unplug your trailer cord from the truck (no brakes) and see if it persists. If yes, then disconnect your battery which will disarm your breakaway switch which I suspect is your culprit. Test your rig in a safe zone.
It sounds like there is an electrical malfunction that is applying your brakes during acceleration; a tough problem to locate. As you accelerate, a circuit closes and the brakes are applied which causes deceleration which causes the circuit to open and allows you to accelerate again repeating the process, thus the jerking.
I had a motorcycle once (BSA Victor) that would die under acceleration, then start up again under deceleration. Quite humorous actually, jerking and wheelies. Turned out the battery was sliding back and forth in the battery box and was shorting against the frame.
