I see how the condo parking lot might be an issue. There really isn't always room for a hauler in those spots.
Stacey....I'd just go to the storage place 2-3 days before a trip and turn on the main power switch, propane, and fridge. Then the fridge should be nice and cold by the time you are ready to leave. Just make sure you don't leave any lights or anything else on to run the battery down. Then, like Joe said, when you are ready to go, your truck will charge the battery on the hauler when you plug in the trailer plug.