The side to side motion wouldn't be because the axles are off center. Something else is wrong.
The easiest way to center the axle is to unbolt the trackbar, then use a cargo strap to ratchet the axle into position. You can put the strap on and move the axle little by little, allowing you a chance to do the measurements to make sure it's centered. Use a torque wrench to reach the 125 ft lbs, not a breaker bar.
But as noted, you will need to look for other reasons for the side to side motion. If the track bar is currently installed, it should be working to locate the axle as it moves up and down.