While I haven't heard that exact comment before, that particular kind of comment coming from a mechanic usually induces me to take a vehicle somewhere else for diagnosis and repair. Maybe (and hopefully) that's not the case here, but to me, those comments are an unscrupulous mechanics' way of implying that the fix isn't going to be an easy one (whether it actually is or not), and that it's going to cost you mucho $$$ (again, whether it actually takes much time and/or parts or not).
Given what the heater did (at least it seemed like that's what you were saying was turning on and off by itself, and not the engine/VX itself), I'd start pulling fuses for the heaters' electrical circuit to see if the problem went away. If it developed some sort of short due to the car washing, taking the short out of the system by removing the fuse(s) might at least help you narrow down what the problem might be.
You can also do a fairly simple self-diagnosis of the alternator by checking what kind of charge it is producing by putting the (+) and (-) leads of a multimeter across the battery terminals with the engine running. A properly working alternator should be sending around 14 volts to the battery.





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