It's an 03 2wd and when I turn right the tires seems to slip like its losing traction. It does not do it when I turn left. Wet ground it's worse but will also do it on dry pavement. Any ideas?

 

I think you are in the wrong section. Do you have a limited slip in the rear axle?

 

Is the left turn out onto a road and therefore a larger turning radius than a right?

 

Yes

 

I would say that it sounds normal for a limited slip diff. The tighter the turning radius the more difference you get in left and right tire rotational distance.
Also the torque caused by towing a heavy load or acceleration in a tight turn will also cause the tire to either slip or slip the clutches inside the rear diff third member.
This is very noticeable on the duallies with a load on the tires they have a great amount of friction against the rear differential clutches.