Traditionally you might expect the car to charge the caravan battery whilst towing, but many modern cars now have "Smart Alternators" which do not constantly produce power so it may be uncertain if your car is charging the caravan battery. You might ask your car dealer if yours has a smart alternator, or if it can be programmed to keep the trailer battery wiring active.
However regardless of whether the alternator is charging the caravan, a 3 hour trip may not be enough to fully replenish the battery, so it is potentially a good idea to at least periodically charge the battery whilst the caravan is in storage.
The other thing to do,is to make it a strict routine to check that all appliance's have been turned off when you put the caravan into storage. Some caravanners discover there can be parasitic 12V devices (tv aerial amplifier is a common one) However you may need to leave your alarm system connected if that is a criteria stipulated by your insurance. Check with your caravan dealer about how it is powered.