If you are having 2 different voltages, even while the car is running, then you have an issue with wiring.
-Take your dmm and measure from the + stud on the alt to anywhere on the engine block while the car is running. This will tell you where your alt is actually sitting.
-Then measure from front battery + to -. If it doesn't match what you measured at the alt, then you have a big 3 wire that is loose or corroding.
-Now test the back battery voltage. If this doesn't match the other 2, then you have a bad connection to the back.
As much of a pain in the ass it is, take a wire brush and clean all the connections, from + connections to grounds. Make sure all paint is sanded off at every ground. And get a new voltmeter.
Good luck