If you are pulling power from the battery, whether by running it directly from the battery or on an inverter that is pulling from the battery, you will be pulling almost 20 amps from the battery. There is no way around that. It is basic physics. Actually, using an inverter is worse, because you also lose almost an additional 10% due to inverter inefficiencies.
As far as running wires to a second battery to charge it while driving, many of us do that. We call it having 2 batteries. We wire a pair of 12v batteries in parallel, or a pair of 6v batteries in series. Use the biggest wires you can find. I, personally, would not want anything smaller than 0 gauge.