The differential is bolted to the chassis. Unless the bushings in the "batwing" mount are shot, there's no way for it to be out of position.
The tires/wheels are located by means of the half-shafts themselves, and the strut rods. What your issue is is most likely an alignment problem. If one side has more positive camber than the other, the top of the tire will be leaning into the car, away from the fender. This could account for the difference side/side. If you stand directly behind the car, you might be able to see the tire leaning in on that one side.
Might just need an alignment, but you also need the bushings in the suspension components checked carefully first.
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