There are very few things left to check, but the voltage of the audio signal feeding the amplifier is one you didn't mention testing yet. A quick and simple thing to try is play the same test tone in both cars and measure the AC voltage at the end of the RCA cable that plugs in to the amplifier. I have a feeling your Car will measure much lower than your wife's car.
You could also try playing a signal from a cell phone or portable music player instead of using the car's radios. Be sure to plug directly into the amplifier though, do not leave the MS-8 in the signal path. You mentioned when you tried this the Speaker made almost no noise, which is a big flag suggesting you investigate further since the headphone jack on a phone has plenty of signal to drive an amplifier if you turn the gain knob up high enough.