When turning left or right forwards or backing up, it really jerks bad.

Replace your 4 wheel drive actuator. This is only a $150 fix and is an easy 20min DYI replacement! Don't pay $2500 for a differential!!!The part is available on line at most part stores.

The Saab 97x is known to have that problem, a rebuild unit is about $1200 - $1500 + labor to replace