Back wheel problem

Sounds like the wheel bearings are bad. These are sealed assemblies that must have the spindle nuts tightened to a very specific setting to hold them together. The most common cause of failure, especially when this happens to both of them, is the spindle nuts were not tightened with a click-type torque wrench.

Is it costly to fix this problem?

You need a live person to look at it to be sure it needs new bearing assemblies. The people at any shop should be able to give you a rough estimate on cost. The online parts supplier I use for reference shows these as costing around $50.00 each, plus shipping, which is about half of what I expected. These complete assemblies cost more than the individual bearings Chrysler used up through the 1980's, but they are a real lot easier to replace. Assuming the spindles are not damaged, I suspect it should take less than an hour to replace both bearings. My concern is if something happened to the brakes while these parts were wobbling around. This is where you need to have everything inspected while the bearings are removed.