Way back in the 70s, when alternative power [electricity production] was nowhere near the sophistication available today, there were kits one could buy to do something like this, i.e. have the car battery serve as an elec. source when one returned home in the car. Or use an additional battery, such as in your case. I never did this, not enough power and not enough driving.... Plus, you need some pretty hefty cables/wires to run from your car to the inverter. Unless the inverter is right outside the car and then you are running 110 v. on into the house, which wouldn't need huge gauge wire.
Like I said, I never did this, but reports I read indicated people were pretty low on power unless all they ran with the system was maybe a small radio and a light or two. These days, a laptop would work, too. In addition to big wires, be sure to secure those batteries well. In a collision, things could be very bad with acid flying around, or the weight of lead/acid batteries hitting the back of your head. Or just spilling acid inside the car and ruining stuff. Personally, I'd spring for even a small, relatively inexpensive solar panel instead. No gasoline or diesel costs, ever.
