Q: When I come to a slow stop, my car starts rocking back and forth.

Typically this type of concern would come from bad misfires as the engine and transmission internals are likely the only parts of the vehicle in motion while you are stopped. Misfires would normally cause a check engine light so you should have the engine mounts, braking and suspension systems checked for problems. A faulted engine mount could cause the engine to rock back and forth and you would feel this motion inside the cabin. Consider hiring an experienced technician like one from YourMechanic who can come out for a closer look at the vehicle to offer a more personal diagnosis of your braking or suspension concerns.