Well, this was covered in a lot of other hardware posts but.....
You got some serious issues.
Im guessing your using an inverter.
Has the problem just started, or is it alwayse like this ? How much other stuff is running off your car ? ( CB, Amps, fog lights Etc. )
Without the answers to those questions, I would say you have 2 possible problems .
Your alternator is overloading. or your batery is just going bad.
Take the car in and ask them to check the electrical system.
If the electrical system checks out, and its still rebooting, your inverter just sucks.
The thing about adding a batery is :
In a 2 batery setup, you normally charge both bateries while the car is running, and run some sort of accessory off the AUX bat when the car is NOT running. If the car is having trouble charging 1 bat and runing the computer, I doubt it can charge 2 bateries and run the computer. Unless the second batery has a lot of amperage.... But I think you should have the alternator / exectrical checked first.
Techonlogy on Wheels