No, the PT shouldn't be going down the road wallowing from side to side and there's nothing to adjust.
Sounds like the struts and shocks have worn out. A lot of us changed up to Tokico gas struts and shocks for better performance especially when we lowered the cruiser with a lowering spring kit. You don't have to lower it but the new struts and shocks will give you a better, firmer ride. Here's a link to what we used. You can shop around for better prices.
Chrysler PT Cruiser Tokico Shocks Struts