It is not normal for the differential to get that hot - even if you drove for 8 hours.
I suspect that the shop did not change out all of the "bad" parts after the accident - expecially if you have a vibration problem.
I replaced my differential on my Chevy Astro recently and there are critical adjustments (gear backlash & bearing preload) required to properly setup a differential.
The differential should get slightly warm after driving 10-15 miles in freezing weather. It will get warmer driving at highway speeds then driving at slower speeds.
I would recommend having a shop familar with MB cars (not a body shop) look at the vibration and excessive hot differential problems.
1998 Mercedes E320, 200K Miles
2001 Acura 3.2TL, 178K Miles
1992 Chevy Astro, 205K Miles