It's a tricky thing to diagnose over the internet, but certainly the rear swing arm suspension design does have it's handling quirks!
A car with as short a wheel base as the 500, with the antiquated swing arm suspension design may well need numerous course corrections mid corner due to the limitations of the design. As an exreme example, if you've ever watched old pre-war race cars, those drivers are sawing wildly at the wheel to keep the car on line going round the corners, and that's pro drivers in well set-up cars!
There's a large rear toe angle and camber change throughout the suspension travel, so this does result in bump steer. My 500 requires a bit of course correction every time a mid corner bump is hit. This can also mean as the weight of the car leans into the suspension the two angle and camber changes which in turn changes how much the car is turning.
But obviously, if you're doing a moderate speed and not pushing the car then you'd expect it to react predictably and you have to trust your gut if you feel something is wrong.
Worn suspension arm bushes could allow some movement changing the rear wheel toe mid corner. There is also some toe adjustment built into the forward suspension arm mounting, if this adjustment is out then that could result in strange handling. Blown dampers could also allow the rear wheels to move unpredictably.
The rear suspension is very simple, even more so than the front, so if you jack the car up and have a look, then a problem should hopefully be easy to spot!
