So the first problem is that the tires were coming apart on the highway? And then the driveline failed? (How did it fail, did the joint break?)
The shop said that tires were coming apart at highway speeds, yes. The U-joints broke and a transmission mount broke as well.
It's not a bad idea to check the rear diff, especially after having a failed driveline. With the tires in the air it's easy to spin the driveline flange by hand and feel if the bearings are grunchy, and it shouldn't have any play in it. The CV joints going to the wheels do have some play normally. Also check the backlash, the flange should turn just a tiny bit before you see the inner CV joints move.
The bearings do not feel crunchy when i spin the driveline by hand. There is some play went i change direction of the drive line, maybe one or two degrees.
I honestly can't see how the driveline or rear diff could cause the rear tires to come apart. I would figure the tires were bad (internal core separation), maybe the wheels are bent, or remotely the bearings/hub could cause it. Did you run over anything that could have caused the tires to fail?
I'm not sure I understand how different sized tires would cause this, but the vibrations went away with new tires.