It turns out that, thanks to the 3G Microcell support forum, we might have discovered an explanation for the problems we've been having with the microcell.
If, while the phone is connected up to the microcell, you have the cellular data switched on, that can cause the audio of the call to get garbled.
To test this out, I called my parents' house several times and had them recite poetry. Those calls where the cellular data was enabled suffered periods of choppy audio, and those calls where the cellular data was turned off did not.
Furthermore, while the cellular data was turned on, I turned off wifi and ran a speed test. That, however, did not induce the problem. So it's not all data use during a call that causes this problem, but only certain data. My speculation is that it has something to do with either location services or push notification.
The workaround for now is to disable cellular data while at home connected up to the microcell. This is not really a very good workaround, however, since the steps to go turn it on and off are 3 levels deep in the Settings app, and without cellular data turned on lots of capabilities of the phone are unavailable.
Hopefully, AT&T will figure out what's going on and fix it sooner rather than later.