OK well are you talking the front tires NOT pulling or rear?
helps to know this, so can give suggestions LOL
I am guessing you mean front as your putting in, but there is a weak link on right side rear axle seal that is known to fail and stop rear wheels from turning,(rusty splines tend to be the issue on back)
up front, I would say, since it doesn't have a locker, that its rather normal for only one tire to turn under power like, and can hold one back
but splines on axles can also be a issue for front, but it wouldn;t make since if your getting them to turn as you apply more throttle and they DON"T slip, but rather grab as your saying it??
that seems odd to me, as if it was splines on axle, or even a diff gear issue, more power should NOT be helping things grab more, , would think slip more not grab better??
are CV joint boots good and solid, and are all wheel bearings good?