The rear suspension on your car did not have air bags. It has springs and air shocks. When the air shocks are pumped full of air, they raise the rear suspension. You car uses an ELC (electronic level control) sensor behind the rear driver'* wheel to detect ride height, that sends a signal to the on-board compressor when the rear is low, which then pumps air into the shocks. If the back end of your car is riding low, and it bounces like a school bus, either the ELS/compressor is not functioning or you need new shocks.
Do you hear the air compressor running when your mother-in-law sits in the back seat? Follow Justin'* suggestion on moving the ELC arm (I think its on the driver side Justin) to see if the compressor comes on or not.
Look at the rear shocks. Are there plastic air lines going to each one? If not, the previous owner removed the air shocks and installed standard ones.
My guess is the original air shocks started to leak, which caused the ELC to run the compressor constantly, which caused the compressor to fail. To get back to original you would have to repair/replace the air compressor, and replace the shocks for air shocks. Or, as Justin suggests, install air shocks with lines that go to a Schraeder valve in the trunk. You can manually adust ride height by releasing air through the valve (just like a tire air valve) or pumping air into it using a compressor (gas station). You would lose the automatic level control, but save a lot of the expense.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)