The in and out play would be c-clip or a diff issue. Best to tear it down to inspect. If there is up and down play then you could have bearing issues too. The in and out could allow water in to the diff kind of like a pump.
I would do a locker test and make sure the locker is working properly:
Jack up the rear end and put it in neutral.
Rotate one tire in the forward direction, the other one should rotate in the same direction. Have a friend hold the left tire and the rotate/rock the right tire in the other direction. It should break free and you should be able to spin them in opposite directions. Then rotate the tires in the same direction and it should lock up again. Then try it again on the opposite side. Try to listen for any weird noises while you do this. You will most likely hear a ratchet sound when it unlocks.
Pull the cover and look for chunks of metal. Move the shaft in and out and try to determine where the play is. Is the c-clip broken? Does the side gear move too?
Post more pics when you do this and I will help you out.