The computer does not control alternator output. It has to be higher than 12 volts or the battery won't charge. I have gotten bad rebuilt alternators in the past.
I would hook up a voltage meter to the alternator that I could monitor from the cab. Maybe also on the battery. At least this might eliminate those two.
An intermittent short could cause a problem like this also. They are the biggest headache ever. Dealers will just start replacing wire harnesses.
I'm sure you've already looked, but a small rub through that is grounding out could do this. Also, a pin in a wire connector that is loose, dirty or bent can also do this.
Since you are having issues with electrical that is all switched from the cab I would go over the wiring and switches in the cab with a fine toothed comb. Hopefully it's not your your left side panel going bad.
I had a blade connection in one machine that was loose. It was causing all sorts of problems but it was intermittent so I couldn't find it. After I started pulling all the connectors, one at a time, I found the loose one, crimped it tight, and the problems went away.
Good luck