BTW, The tough guy above wasn't me... You're just looking for simple help. And some know-alls tend to get short and snippy. My apologies. I hope I can better explain things in this long response.
ALL your lights are 12 Volt. Your furnace fan is 12V. Water pump is 12V. However, your fridge is probably switchable from 12V-to- 120V-to-propane. They all need at least a battery to operate.
(Plugged in, your lights should work, with OR without a battery installed,) While PLUGGED IN to an extension cord, your hidden magic "power converter/battery charger" kicks in automatically, knocking down the 120V "shore power" to 12 volts, it'll power the 12V lights, 12V furnace, 12v fridge. Trailer plugged in, your converter/charger will also do its best to charge and maintain your newly installed $200 Optima batt.
While it sits in the driveway, keep the trailer plugged in to 120V (all spring, summer and fall) so the charger can maintain your 12V Optima blue top batt. (Make sure your lights, fridge and everything else is turned off when you shut the door. And make sure the cat isn't in there!_
When you're "boondocking" (ie out in the forest withOUT any 120V plug in), your 12V batt is ALL you've got for lights, furnace, 12v TV, water pump. Be miserly with lights, and your battery should last 4-6 days in the forest. So MAKE SURE you put the FRIDGE ON PROPANE at once. A fridge on 12V will KILL even the best battery in 6-8 hours. (Other hand, if you're "plugged in" at a KOA, by all means click your fridge to 120V to save propane.)
Of course while you're driving, you can run the fridge on 12v again.
(Remember a good battery deep cycle recharge can take 24-48 hours.) Relax- camping is supposed to be fun and as cheap as you can make it.
