The problems you're describing are due to the extra weight in the car causing the suspension to sit too close to the bump-stops.
This restricts the available travel in the suspension and will make the ride over rough roads very harsh. The shock absorbers will play no part in this, although they will allow more body movement if knackered.
Sounds like the springs are sagging............as said elsewhere, check the ride height and replace with standard spec ones if they are sitting too low. Anything "uprated" or sporty will decrease ride comfort significantly.
In England, a leaking shock absorber will fail the MOT test.
'73 Jensen Interceptor (Resting)
Giant Full Sus Mountain Bike