You said it shook? Would that be a front to back or a side to side? Was this felt in the body of the car, in the steering wheel or both?

Have you checked your brake lines for kinks??? Both metal and rubber. You could have a kinked line on one side. If so i would imagine that if you've touched the brake peddle then the fluid would get trapped, when you stop or let it sit that allows the fluid to slowly get released solving the problem. It would happen fast enough for you to not be able to check it unless you see the line, and it would explain both the shake and the car straining...

Check the metal lines under your car tooo...there are metal lines down there that could have been pinched. i think if you scrubbed on something or especially if you bottomed out... Just some thoughts...trying to help and all...

That last thoughts i have are some sorta strange brake booster failure of some compltetly wierd sort...or like ABS pump mess up, but idk if yours has ABS, and i know nothing about ABS...

Other than that i got nothin...
I love my car...
I love Horsepower...
I love reliability...
So why do i own a DSM again?