I'm curious to know more about what you're trying to do. How are you going to keep the battery charged?
There's probably a way to get power out of the battery but it's almost certainly not going to be the proper voltage for your inverter. Since you're talking about an inverter, I assume you want to go from your battery through the inverter to get 120v AC? If that's right it will be way more efficient to get your AC straight from where you plug in the charger for the battery.
What's an eco-cottage?
TT