12v furnace install in a park model. (120v) need help

My furnace pulls about 5 or 6 amps if I remember right. You current battery and charger are not nearly enough.
I would just use a 12v power supply and forget the battery. Radio Shack has some. Astron is an excellent brand. I would look for something rated at least 8 or 10 amps as a guess. The best way to size it is either find the label on your furnace or measure the current draw with an amp meter.