Rear end problem?

My 95 5.0 5spd has a factory rear end and very minor bolt on mods, my traction loc works fine if I spin in a strait line or if I hang a donut to the left but if i try to do a donut to the right or hang a figure 8 it just kicks to one tire. Also some times when i spin in a strait line and turn to the right slightly it will kick to one tire. My car has around 70,000 miles on it and was babied until I got ahold of it, any help is greatly appreciated.

Ok what kind of fluid do I put in the rear end and how much will I need. Also is there a special additive to put in the rear end when I do the change??