My car cuts off when at a stop and when I change gears (sometimes)

not said year could be the cam and crank sensor. also you not said what gear box you have auto or manual. auto its down to having a ecu problem with it being in limp mode. manual it will be the same but more manageable with your onwn gear changes.

car is not warmed up enough or your idle is to low, also might be a alternator problem

Our Jeep would cut out at different times and die or sometimes just cut out for a second or two, I replaced the Engine Position Sensor at the Bell Housing on the Drivers Side and it took care of that misterious problem.

You mean sometimes it wont get out of its own way and other times runs like a bat out of hell from a stop ? Sounds alot like a bad Mass airflow meter or it isn't shifting down into first gear. Try manually selecting low gear when you start out and see what happens. Also low fuel pressure or very restricted fuel filter can do this too.

Sounds like a symptom of a low fluid level or either a clogging filter. Change your fluid and the filter, and see if this doesnt alleviate your problem.

Any time the transmission goes into the limp mode, it generates an error code that tells what caused it to go into limp mode. It could be something as simple as a loose connection on a sensor for the transmission computer. The code would explain which sensor was sending the correct signal.
By restarting the car you are resetting the transmission computer, clearing the limp condition.

if you are only having the issue in reverse that would make me lean more towards the transmission having an issue than the clutch.

If its the 4JX diesel engine the crankshaft position sensor wants an adjustment as its going out of range.

change out the fuel filter... that should sove it... if not... it's the fuel pump

FIT NEW VEHICLE SPEED SENSOR THAT SHOULD FIX IT