the shaking seems to match the axel speed and it happens when there is a load on it.

 

I had this problem or one very similiar to yours. Turned out that I had one or two (can't remember) bad cv joints. The joints were so worn out they caused the motor to shake as well as and uncomfortable shake in the cabin. If yours are about due to be replaced go ahed and do both regardless. Night and day difference for me. Hope this helps.

 

that was my first thought- cv axles assembly
dont bother trying to do one,,
replace complete unit with NEW one from parts stores like napa
under 100 bucks for new shaft- 2 bearings 2 seal boots

 

Motor mounts or axles.

 

My guess would be motor mounts.

 

x2 on motor mounts.

 

I vote front axles/cv joints. It seems I have read more about bad motor mounts causing hard shifting from R to D, and it would also seem that a bad motor mount would shudder while revving in P. OP only mentions shuddering while under load. And, I have had the same symptom in other cars, and it was the axles. Just my

 

Have you recently had your EGR ports cleaned?

 

Please elaborate...not trying to be an ass, but just wondering what was your reasoning.

 

plugged egr ports mess up engine running--needs cleaning every 75kmiles
see diy for pics as proof of crud buildup