Best way to run the Fridge

We are very new to caravanning and would like some advice on running the fridge. we have been towing with the electric of the van switched off, when arriving on site we hook up and switch the fridge on, it then takes so long to get cold when away for a weekend it is time to go home by the time the fridge is at optimal temp. We have the van in storage so cannot hook up before towing. should we have the electric on whilst towing? would that use the leisure battery or the car battery? I would really appreciate advice.