RV dog trotting.

On my trip to Dallas this past Tuesday I noticed my coach was "Dog Trotting" down the road (the only way I know how to describe it). Also when braking the rear of the coach felt as if it was "fish tailing. There is something loose or broken back there. It feels like when the rear wheels start sliding when on ice or wet surface and you would steer into skid to correct. Any one have any idea what I should look for first, and where I would have it repaired?

1999 Monaco Dynasty 40'