This is probably too easy but worth a shot.

The same happened to me while driving to SoCal....it started to shake and I slowed down, I started going faster and it shook so hard that I thought either it was going to flip over or the whole rear-end was going to fall off.

It turned out that one of the tires was starting to separate.....fuuny now...not so funny in the middle of the desert.

P.S. make sure your spare is filled with air....some people (like me) have to learn the hard way.