Do you have a Detroit Locker?

Quite normal. Driving a rear Detroit requires a gentle throttle foot. In corners and going around turns, keep a steady speed. Do not accellerate or decellerate. If you must slow quickly in a turn, do it all with your brakes by stepping on the clutch. Get in the habit of either using or being quickly able to use the clutch in turns, because if the locker fails to unlock (pressure on both wheels and the engine because you are using too much throttle or not enough) and the road is slick from rain, snow, gravel, oil - whatever, you can loose control quite quickly. The locker only unlocks for turns when the engine isn't forcing it in either an accelleration mode or a decelleration mode. It really doesn't unlock at all. What actually happens is that the wheel that is turning faster because the road is forcing it to turn faster (turns) ratchets or over runs the locker. The engine will prevent this ratchet action by putting pressure on the axles, and it can do that by drag (decelleration) or power (accelleration).
As far as pulling to opposite sides in heavy acceleration and the opposite side in deceleration, my guess would be that it is caused by the tires not being exactly, and I mean really EXACTLY the same diameter. If that is the case, I doubt that you could ever get the tires exactly equal enough to stop that action, and even if you could, it wouldn't last very long.

Doug '97 TJ
Creator of the CBrack
CBrack.com

Could be either, but probably engaging. When you go around a corner the outside wheel rolls faster. The locker, IF IT IS IN A NEUTRAL CONDITION, in other words, power is not being applied to increase the speed nor is the engine dragging it down to slow the vehicle, it will allow the outside wheel to roll faster than the inside wheel. The locker is not actually "unlocked". It ratchets kinda like a ratchet wrench when you reverse the direction from the torque direction.
You shouldn't normally feel this ratcheting action. Might hear it, but shouldn't feel it. If you allow the engine to affect the wheels, in other words, you accelerate or let the engine slow you down, the pressure causes the ratcheting to stop and both wheels to become solidly locked to the engine once again and begin to roll in sequence whether you are through turning or not. At that point one of the wheels has to loose traction, either spinning or sliding depending on whether you are accelerating or decelerating.
This is an explanation (simple explanation) for a full locker like a Detroit, not one of the other types that may use clutches or some other method to lock.
The confusion arrises because some lockers actually lock up when conditions dictate (ARB, clutch type etc) and others are locked all the time like the Detroit. The ones that are locked all the time have some method to allow the street to dictate an over ride condition which means that the momentum of the car rolling is the imputus for causing some condition to exist in the locker as opposed to engine power. As long as the power derived from the momentum of the vehicle's movement is greater, the locker will be loose enough to ratchet. When the power from the engine is greater that the momentum power, the engine dictates and the locker has only one choice - locked. Well, that's not entirely accurate. The engine power just prevents the ratcheting from taking place.
Suppose you were tightening a bolt using a common ratchet wrench. But suppose that bolt was turning in the same direction at 5 rpms. As long as you turn the wrench at greater than 5 rpms the bolt will tighten, but what if you were turning the wrench at only 3 rpms? The bolt would not tighten or loosen. You would just hear your ratchet clicking as the bolt out ran your effort. That's the principle of the action in the locker.
Hope this helps.

Doug '97 TJ
Creator of the CBrack
CBrack.com