If your charger works now, you only need to install an inverter. If you have it installed and want a "whole house" solution, you'll also have to install an additional transfer switch or manually connect the shore power cord when using the inverter.
Two 6V batteries will limit your inverter size to around 1000W as a big inverter operated toward the maximum rating will suck down the two batteries pretty quick. Most folks just need inversion for entertainment gear, charging/operating computers, and phones. Small items. You can get an inexpensive transfer switch limited to 15 Amps to run that sort of stuff through a single AC branch circuit.