Sounds like a torque converter solenoid problem.
A quick check is to unplug the square connector on the transmission where the engine meets the transmission.
If you are standing in front of the vehicle, looking straight down on the transmission (by where the transmission pan meets the transmission), the square plug (usually green or blue) should be sticking straight up.
Unplug it and take it for a test drive. If the stalling goes away, the torque converter solenoid will need to be replaced.
CAUTION: Driving extended periods with the connector unplugged may cause the transmission to overheat and do internal damage.
When it starts to hesitate/jerk a little going down the road, step lightly on the brake pedal (only enough to turn the brake lights on). If the jerking stops, you confirmed that the torque converter solenoid is a problem.