It would be unusual for both rear wheel bearings to go "bad" at the same time. As noted, when you sway the car side to side, the offending bearing will get louder when the load shifts to that side and vice versa. Same with the pinion bearing being louder with more power being applied to it.
As I recall, the FSM illustrates how to change the bearing. The "removal" is by disassembly of the bearing, roller by roller. When it's all removed, then the new one is pressed on. Might be some special holding fixture involved?
IF the particular axle shaft has wear, you can lightly apply the brake while driving. The brake shoes will center the axle shaft and remove load from the bearing. If there's a wear trough on the shaft, the noise will be greatly diminished.
In any event, best to get the car to a reputable shop, even a good Chrysler/Dodge dealer in your area, and get the axle lube and such inspected. It would not hurt to change the rear axle lube anyway. With the rear cover removed, you can look at the gear set, too.
With the car on a body-contact lift, you can put the trans in "D", let the engine idle, and use a stethoscope to listen to the sounds it makes and where they are coming from. Look for u-joint possibilities, too.
IF, worst case scenario, you need the pinion bearings, wheel bearings, and the carrier side bearings, it might be about $1k to do all of that. Odds are you won't need all of that KEY is to get it looked at soon as it's not going to fix itself.
When the rear suspension affects the "wander", it's because the rear axle is shifting on its mountings as the wheels might encounter bumps and such. In the case of the Chrysler rear suspension, the main mountings are the front eye bushing and the rear shackle bushings. Check them for cracking and deterioration. On the "Torsion Quiet Ride" cars, of which yours is one, the rear axle mount to the spring saddle has rubber isolation where that all bolts together. If that rubber has deteriorated, it can allow for some movement within the mount by the axle. Earlier cars had more solid axle mounts. I believe one of the suspension parts vendors has some harder rubber isolators, which aren't very expensive at all. The car would need to be suspended on a body-contact lift to do that swap.
ALSO, look at the tires for irregular wear of the tread. One customer came in one cay and wanted a rear wheel hub for his car. Said it was getting noisy. Two weeks later, he brought it back . . . rear tire noise, which new tires fixed.
So, several things which might be causing your noise. Diagnose carefully. Keep us posted.
CBODY67