Can't run a portable freezer on B&D battery station

I take this trip every weekend to haul frozen groceries from Whole Foods Market. My wife would much rather transport them in a freezer, and not in an ice chest, for her peace of mind...

If I was to buy a larger wattage battery station, do you think that would work? Or should I forget the battery station and buy a pure inverter, not a battery station, that can be plugged into a cigarette lighter outlet in the car?