300e '87 dies in traffic.

First a bit of history. The alternator died. The car died when the battery got too low to run the ignition. The odd part is that the battery could crank the starter, but the electronics wouldn't work. The
battery read about 10.5 volts with no load.
I called my wife, we used the truck to charge recharge the battery enough for me to get home before the batter went below 10.5 volts again. I measured the "charging" voltage at 3k rpm and the only voltage I measured was due to the battery voltage, not the alternator.
I replaced the alternator and the voltage was withing specs at 3k rpm.
I really don't know if this related or not. HOWEVER, a few days later, I was sitting in traffic waiting for a funeral and the car died. Thinking I had the same problem (new alternator was defective), I got the person behind me to wait for 10-14 minutes while we used his vehicle to charge my battery. The car started and I went the 2 miles to my destination. I didn't have a volt meter at the destination, but I had a 10 amp charger. I put the charger on and the battery was only drawing less than 2 amps, so I know the battery was charged.
We left later that day, go stuck in traffic once again and the car died. Thinking the alternator was good, but not charging at low rpm, I thought the battery must be too weak from age and the recent abuse. I called for assistance and a volt meter. We waited for about 40 min for the assistance and volt meter. The battery was charged. I restarted the car with no assistance and we drove the rest of the way home.
Still having the weak battery mind set, I replaced the battery. My wife has been driving for three days with no problem... then ... she go stuck in a fast food drive-through line. When she started to drive away, the car died.
She called me. It took about 15 min., I got there, the battery measured 12.6 volts, and I started the car with no problems.
I am now convinced that I had been stuck with the bad battery mindset, and that the original problem has nothing to do with the new problem. The only thing in common with all three times was that it happened after the car was sitting idleing in traffic. (AC was on)
Does anyone have any clues or similar past experience?
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What is your voltage when your car is idling? It should at least be 13.5V and perfect voltage is 14.4 V.
I think your problem is overvoltage relay going haywired on you. It is the relay behind your battery with a red fuse on the top. Check the date stamp on that relay... if it is the same year as your car... then it is time to buy a new one.
You got new battery and new alternator is as far I understood.
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