The motion is probably coming from the rear suspension... from the rods or arms mentioned in above post. Rubber grommets are more than likely worn out and there is now play in the rear suspension. Pull off a wheel and have a look at them. They run from the back of the wheel hub to the frame of the car.
The differential mounds will come out using a 12 mm Allen head wrench or a 12 mm hex socket. The socket is difficult to find and may have to be special ordered.
I bought a 12 mm L shaped Allen wrench at Sears and then cut about an inch and a half off the long end and then put the cut-off piece into a standard 12mm socket. In other words I made a 12 mm hex socket that will fit a rachet.
I'd avoid the differential job if its not necessary. Its difficult to get the new mounts back in.
The suspension job is a must! Make sure you get all the pieces because MB redesigned the bolts and arms. Get back to me if you need help. You will need a star socket to put the new bolts back into the mounting brackets. Can be bought at sears or auto parts store.
1993 190E 2.3
2000 Toyota 4x4 Tundra