I'm pretty sure that model is a fore and aft pivot only with no side to side pivot. Dual Jaw design. This design is pretty strong with the only real knock to it being the lack of side to side tilt. There are thousands of these hitches out there and come up for sale quite often on my local craigslist.
It could very well be that some of the springs have weakened over time or there could be some wear on the jaws. Either way, we need the op to post back some info to help make a constructive set of recommendations.
OP here is a set of jaws off of a new Reese hitch...do yours look similar, can you see if there is significant wear on the jaws that may be allowing the king pin to rattle around too much?
How about the hitch itself, when its pinned into the rails how much movement can you feel just by pushing on the hitch?
Thanks!
Jeremiah