Why are you disconnecting the battery? On mains hook up, the charger will deliver 12V to the caravan and charge the battery.
You will have to disconnect things in turn to discover what exactly is tripping the mains.
Insurance is far more than just finding a stolen caravan. Do you want it back if some nasty person has ruined it inside?
Insurance is about repair and/or replacement.
In my biased opinion, I would go for insurance before tracking.