I KNOW WHAT HAPPENS TO A 4 WHEEL DRIVE WHEN YOU HAVE DIFFERENT TIRES AND THE EXPERIENCE YOU SON HAD WAS JUST THE SAME / I HAVE RECENTLY LEARNED HOW CRITICAL IT IS ON AN AWD IF YOU HAVE MORE THAN 2/32 OF AN INCH SUCH AS TIRES PARTALLY WARN AND YOU GET A FLAT YOU DO HURT YOUR DIFFERENTIALS WHEN YOU DONT REPLACE ALL FOUR TIRES
After thinking about this a bit more and going back over all of those pictures closely, I’m not only going to back up a step or two but will say that I retract my last opinion on this matter and state that I was wrong.
Sears screwed up, no doubt about it. However, I don’t think the differential explosion was caused by the tire size difference. It appears to be lack of gear oil, pure and simple.
Heat can develop in the differential due to tires but this thing is beyond that. It has been fricasseed. This had to be an accident waiting to happen and by coincidence it occurred after the tire installation.
One wonders if this vehicle had been low on gear oil, or getting low on oil, and the gradual gear whine that developed was tuned out by the driver. It’s similar to becoming acclimated to shocks or struts getting weak. They grow on you gradually.
I don’t think the OP has a snowball’s chance in of winning a case in court.
It would still be interesting to know the details behind the salvage yard replacement.