Help! Electrical problem

Car: 2009 Aveo5
Problem: Battery and brake light illuminate together. (Bad alternator)
Story (In a nutshell): Battery and brake light came on. Dash lights started to fail. Gauges started to fail. Engine stopped. Stalled on the freeway. Nice people helped me push to a hospital parking lot. Jumped. Started and ran for a few minutes then died. Repeated this about 5 times. Went to store and bought a new battery. Car started and ran but lights (battery and brake) remained on. Drove home.
What I've done so far:
- Checked all fuses - OK.
- Got a new battery.
- Removed alternator, took it in to be rebuilt, reinstalled rebuilt alternator.
- Tested wiring from alternator to battery - OK.
- Tested voltage running should be about 13.7ish volts but am getting intermittent readings of ~13.2v.

Existing problem:
It seems that the alternator works but there is something happening that "turns it off". While it is running, the engine changes pitch (like when the A/C compressor kicks in) and the voltage drops and the batt/brake lights come on. It runs like that for a few minutes then the voltage goes up over 13 again and the lights go off. Repeat...repeat...repeat. It also does it while driving. I tried to connect the problem to RPM but it seems random.

An electrical engineer friend says that there should be a electrical charge control module that regulates charging the battery. He's not a mechanic but says that's the way recharging works.

At this point, I have eliminated battery, alternator, fuses, and wiring. What else is there?

Is there a relay, fuse, ECU/ECM, or other component that I cannot/haven't checked?

I dread taking this in to a mechanic/dealer to get it diagnosed since I'm a po' boy.

Ideas?

No reason to eliminate the alternator as the problem, because it's entirely possible it was not properly rebuilt. Take the vehicle back to the shop that did the rebuild, explain the issue you're seeing, and ask them to test it. BTW, the component you're friend mentioned is the voltage regulator; is located inside of the alternator case; and could (if defective and not replaced) could be the cause of your vehicle's issues.

Fixed! Thanks avguy!

I took it back to the rebuilder and they tested it again. It was good initially but I had them run it on their machine for a while. After about 5 minutes, it failed. They said that some of the circuitry inside was burned out. They gave me a new one, I installed it, and it works perfectly.

A side note that the tech told me was that we already understand that a bad alternator can kill a battery. But it also holds true the other way around. He said if I had a bad battery, with some dead cells, it could lead to this problem of the circuitry burning out in the alternator. Good to know!

All-in-all, it was a good car day for me.

I also have a problem that started with an electrical issue. Power Window would not work and was blowing the fuse everytime I used the Drivers side window. Mechanic said it needed a Wiring harness and a fuse box that is located in the engine compartment. Well they couldn't find a harness so they decided to rewire it without the harness. (forgot to say the ONLY issue I had was the Power Window Fuse kept blowing,everything else worked fine) I got my car back and the A/C didn't work. that was fine because my window now worked. Well a few days later my window fuse blew again but my A/C worked now. Well I replaced the power window fuse and the window worked but my A/C wouldn't work again so back to the Mechanic I go. They say it is the computer so now I get hosed for a new computer. Oh and by the way my gas gauge didn't work after the rewiring and I have a check engine light on. so the other day (After 3 Months) I'm at a red light and all of a sudden the engine started to buck and the check engine light starts blinking......Well back to the Mechanic. They Replaced a Sensor and the car worked fine until after about 20 minutes of driving Check engine light starts blinking and the engine sounds like a motor boat. So Once again back to the Mechanic.......Now they tell me that there are codes being spit out from the Fuel Sending unit to a transmission problem and he tells me that it is not worth putting any more money into the car. My Question is......Could all these problems come from the rewiring of the Door and the fuse box? Or do I need to take my Aveo with 263,000 mile on it out in the back and put it down? I was seriously thinking about getting a remanufactured engine (Not a rebuilt engine). What are the thoughts in here?