Here is how to tell if you have a locking diff, jack the car up from the pumpkin and turn one rear wheel by hand, if the other wheel turns in the same direction then you have a locker/posi/etc. If it is a locker the shudder could be from the discs and you do need a special additive. If you have the one whell wonder type then the other wheel will turn in reverse. Look at your spring hangers and make sure they are plumb look at and try to move the banjo from side to side U joint could be bad tranny mount could be broke the whole shudder sounds like something is coming out of alignment.
JimG