Radio shuts off when in drive, alternator voltage is low?

You solved our previous problem with the code and noise. Thank you. Our original problem still exists: The radio, which works fine in park with engine on, but once I start driving straight, it shuts off and comes back on when put in park. My son just installed a new alternator, battery and new pos and neg battery cables. However, the new alternator reads at 12.6 volts. My son had AutoZone test the alternator when he bought it and they said it tested just fine. He even tried another new alternator. He says that something is keeping the alternator from reaching 13.5 or higher volts when it's in the car. I don't know if it matters, but the radio controls on the steering wheel no longer work. I can live without a radio just fine, but I don't want to be stranded. Can you please help?