The real issue here, is that your symptoms are a mix of a bad traction control relay and a bad engine control relay (both on the RCM) and a weak battery and/or bad battery cables or maybe an alternator that is undercharging. FACT IS: You have a fundamental issue with a lack of clean, stable battery voltage in this car or you have a really bad RCM.

A few suggestions:

1) Get one of those snazzy cigarette lighter voltmeter thingys and see what system voltage is with the engine running - anything below about 13.2 is a suspect and anything down below 12.5 or so is a problem. With engine at 2000 rpm, you better see 13.8 to 14.2 volts. You are testing the alternator doing this. Alternators are easy: They prop system voltage up when ever the engine is running, if the alternator cant do that, it's bad. Yanking the alternator and having a local shop rework it is preferred to replacing it with one from Autozone/NAPA/Etc.

2) Replace the car's battery. (If you have it "tested" and the guy tells you it's fine, please don't ask for tech advice here, I told you to replace it. You can't effectively 'test' the battery for what we are chasing - do not expect the 'tech' to understand things like capacitive reactance or noise immunity.) While you are at it, make damn sure the battery terminals are clean and tight. If the cables look like hell, get them replaced, PERIOD. Don't avoid doing this because "its too hard" or "the shop says they are OK".

3) Yank the RCM and send it to DJ. (Do this even if the above fixes the car, our RCMs are known failure items and you should have the RCM reworked at least once in the car's lifetime. DJ is one of few members capable of doing this effectively.)