As you say its how long is a piece of string, there are so many variables its impossible to say, but a new battery should last better than old battery, But assuming there is nothing draining the battery you should be ok with 3 to 4 months could be longer but its that length of string issue again.
Just for your information, using a mover for a few minuets doesn't need massive battery capacity, and most people will user thes than about 2Ah of battery capacity. As an alternative, if you arrange to have the mover battery wires easily accessible when the caravan is in storage, you could bring a small car starter battery just to move the caravan.