I have never had one do this. I am thinking AWD clutchpack failure. Seems to mostly go away with the FWD fuse installed on the 4EAT transmission.

Not exactly sure what you are trying to describe here.

The car actually pulls to the side when it shifts, sort of like a brake caliper hanging. It actually kindof swerves!

Ok this is interesting.

 

How many miles.

 

That sounds more like something loose in the front end, a loose engine, first thing is get under the car with the wheels off the ground (not running) and inspect everything.

Tires? Accident damage? Bent/loose suspension parts? Loose nut behind the wheel? :-p

Alignment specs would be interesting to see.

What about axles?

Sounds like to me something is really busticated. My fist thgout too was "when was the accident"

Check the lower control arm bushings. They may look good but I'm willing to bet the rubber is starting to split and they will puke the oil out shortly there after.

Shawn Have seen before think it was bad DOJ Mike.