I think you have a charging problem. If the charging system isn't keeping up with the amount of power being used while driving, the battery voltage drops. How fast that happens depends on how many accessories you have turned on. By turning off the heater while driving with a low battery the lights would get brighter, less load. If it was raining he probably had the mode switch dialed to defrost .If so the A/C was also in play. More voltage drain. If you had a short in the heating system, you'er be popping fuses. If you had a draw heavy enough to drain a battery while driving it would have to be the blower motor and it would not be putting out very much air flow and it would be making a lot of noise. Pretty soon you'ed smell smoke coming from wiring, the wire insulation would melt, you'ed get a short and the fuse would pop.
If this vehicle is a stock vehicle, when you changed out the alternator you unbolted the heavy hot wire and unplugged a two wire connector. If the wires didn't fall out of the connector its wired correctly. I'd do a load test on both of his batteries. If they check out ok, I'd look real hard at that alternator.