95 caravan engine shakes from side to side

Dear all,

Here is my story:

I have a 95 caravan with 3.0L and 3 Sp. transmision wiht 145km.

>From day one, for 5 months, I had a grinding sound when I accelerate
from stops, and I think It comes from transmission/differential box.
It might be related to the problem but I do not know. I checked the
hub and bearings and they are ok.

2 weeks ago, driver side CV started to act up. It stuck at different
positions, however the boots are good. I changed it. After 50 miles,
my car started to shake at 30 mph under load very badly. If you pass
30 mph point, even at 70 it does not shake if you dont put car under
heavy load. I do not feel any shaking on steering wheel but whole car
shakes, swings. I raised the car and watch which part shakes. It was
engine going from left to right, like 1 to 2 inches.

I took the half shaft out put a new one it. Now it does not shake that
badly but I just put on 10 miles yet. It might show up later.

My questions, does the differential box on transmission might be the
reason for this thing?

I donot know any parts that will make the engine or transmission swing
wildly from left to right. Any rotating parts should make the engine
swing from back to front, or up down.

Can i change differential on this cars without removing transmission
from the car.

Thanks for the inputs.