I used to own a 91 300TE 4matic, and experienced the same "shuddering" symptom when backing out of my driveway. It would only happen about half of the time and was generally more pronounced when I was backing to the left. I took the car to the dealer here in Cincinnati, and the mechanic drove it, experienced the shudder, and declared it to be normal.
At the time the car had 150k miles on it, and was on it's second transfer case. The first one was rebuilt (resealed) by my mechanic (Precision Motorcar, Cincinnati) at about 90k miles. The second transfer case was installed at 120k and was a factory rebuild using all the latest "updated" parts/seals in it (from what I'm told).
(Both these repairs were done prior to my ownership of the car, thank goodness, as a rebuilt transfer case runs about $2000-$2400.)
I never personally experienced the symptoms of a failing transfer case, but I understand that the classic failure mode of these units is internal and external fluid leaks. I would investigate getting yours replaced (with a factory rebuild) very soon. It's a big financial hit, but that's the price of admission for owning one of these cars.
I had great difficulty selling this car. It had all records, 155k miles, and in excellent condition. The final straw for me was that we found friction material in the transmission fluid (good sized chunks, about 8mm square flat pieces) and it began to show signs of needing valve seals and stems. I could not see throwing another $4000-$5000 on this car for a new tranny and valve work (I had the cam and some lifters replaced two months prior, due to some top-end ticking noises that revealed a badly-worn #2 lobe.)
I was finally able to get $11,250 for the car after three months of trying to sell it. I had paid $13,500 and put in another $3000 during the course of 10 months/15k miles.
Careful examination of the records revealed an ongoing maintenance and repair expense rate of about $0.15/mile, not a huge amount.
But, I drive 20k miles or more per year and could not see paying $3000 per year just to keep that thing on the road.
I then went out and bought an 85 300D for $2500 and have been quite satisfied.