It sounds like you are getting 4wd by they description of the shake when turning a
corner. The sound you get that you say sounds like the t-case coming apart sounds
like the binding and realease of load in the drivetrain. Have a look at your tires, do they
have the same amount of tread left on them between the front and rears? If they don't
then shifting into and out of 4wd can be hard because the ease of shifting depends
on all wheel spinning about the same speed. If the rear tires have significantly less
tread than the front, they will be spinning faster than the front causing shifting problems
in the t-case. Driving on dry pavement with tires that are worn unevenly like this can
damage the t-case due to the fact that two tires are spinning faster than the other, but
because they are all mech linked to each other you get a loading of the driveline that can
then cause a loud bang as something gives. On slippery or dirt surfaces this is not a
problem as the loose ground prevents the drivetrain from loading up. The shake when
cornering is caused by the U-joints. A u-joint, when it is at an angle, speeds up and
slows down as it rotates, this is why the driveshafts have two u-joints, they cancel out
this characteristic but the front axleshafts only have one each. A CV or constant velocity joint doesn't
do that due to its design. The grand cherokees that have full time 4wd use CV joints on
the front axle so this shake doesn't happen. A good safe way to test is to get 4 jack
stands and put your vehicle up and watch for all four wheels turning, just make sure
you shift into 4wd with the wheels stopped as attempting a shift with the rear wheels
turning will give you an unpleasant and loud grinding.
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