Once you get the discs off and get a look at the parking brake shoes then hopefully it will be clear whether it was the parking brake on or the main pads that heated up. I would think the offending pads/shoes would be badly burned compared to the innocent ones. For my blind guess I am going to side with your wife and say that it was not the E-brake but was the mystery failure described by some others such as master cylinder or hose.

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra