Tell us more about your Jeep. Do you have new tires? What size? Lockers? I assume you are in 2WD. Even then a locker will turn both tires the same speed and squeal your tires.
It could be front end alignment. When drive in a very tight circle to the right the right front tire will be going in a smaller circle than the left. A little slippage would be normal. Since you describe a lot of slippage your front end might have too much toe out.