Kate,
The parts that directly and indirectly effect the Ride, Handling and Comfort are all a compromise.
Shocks do not actually absorb shocks...they control and damper the suspension springs Springs absorb the road shocks like pot holes and bumps. The shock only stops the spring from continuing to bounce the vehicle.
Most cars have softer spring rates and soft to moderate shocks for a more comfortable ride...this is a compromise for ride comfort.
Performance vehicles generally will have medium to firm spring rates and shocks. This makes the rider a bit harsher and may not be as comfortable riding to some people, but it allows the vehicle to keep the tires pinned to the road and more controlable.
A sway-bar is a spring steel bar that connects the front wheels together and a rear sway bar links the back wheels together so that if one is going around a corner, the downward sway of the vehicle on one side, is distributed to both sides of the vehicle to allow the vehicle to corner flat with far less sway or leaning.
The Gen-1 Sport Trac has a truck suspension to handle the gross loaded weight and towing capabilities...that means that the springs are much stiffer than a car to handle the extra weight. This means that you will feel the bumps in the road more than you would in most cars.
If swaying is the problem, upgraded shocks and sway-bars can improve cornering and handling, but do not do much for ride comfort.
You are talking about swaying, rocking when going over bumps. That sounds more like a shock issue, but if the shocks are new it should not rock back and forth unless a new shock has gone bad? If you go over a bump with one wheel, the vehicle will tilt slightly and then back again when the tire goes off the bump...this is normal for most truck suspensions but it should not bounce back and forth several times which would indicate that the shocks are bad and not controlling the bouncing of the spring.
Sway bars only help when cornering and do little or nothing to absorb bumps or the side to side rocking motion you experience when you drive over a bump on one side.
...Rich