Hello James,
Yes this sounds like the symptoms. One shock may have completely failed. When you hit a bump the swing axle geometry along with the bad shock can cause this unstability.
You can check to see if a rear shock has compeletely failed by pushing down on one rear corner of the car. After the push, the car should return up and stay there. If it bounces a bit, it has lost hydraulic oil and is bad. Besides hydraulic oil, the original shocks also have a nitrogen charge which exerts upward force and also keeps the hydraulic oil from foaming on rough road surfaces. The shocks may function but can become weak if some or all of the nytrogen escapes. You can check your rear shocks by simply disconnecting them at the bottom (one 17mm bolt). Force the shock bottom off its mounting. If there is still a nitrogen charge in the shocks the shock will expand to full length and resist compression.
These cars were designed to use gas filled shocks. Bilstien are probably the best choice, they are a little pricey. Some performance oriented owners have used Koni shocks which are even more expensive. There are some other gas filled brands which may not be as good and will not last as long.
A new set of gas filled shocks does wonders for a tired suspension. Often times some mysterious suspension noises also disappear.
Original Bilstien shocks and replacement Bilstiens have date codes stamped on them. Look for the two digit year date to see how old they are.
Joe Alexander
Blacklick, Ohio