If I have to use a battery charger I use a C-tek 7 amp multi-stage 'smart' charger. This type of charger can be left connected to the batteries if your car is in storage to maintain them or to operate as a 'normal' battery charger if you have a flat battery. Most times it will put enough charge into a flat battery in about 15 minutes to enable a start (only if the car fires first turn of the key though). This can be connected via the rear Anderson plug. I dont know about charging via the white plug on the rear.
My previous 2 Defenders had solar panels permanently mounted on the roof - an 80w panel up there enabled me to camp for 10 days (maybe longer, but I never went over 10 days) without starting the car using a 50 litre fridge. I am strangely reluctant to drill holes in the RRS though so now use my 80w folding panel but as yet not for extended stays, but it should do the same job.
From what you describe re short or no trips I would connect up a solar panel to the car whether running a fridge or not as I imagine the D4 also uses plenty of electricity while parked.
It really depends on how much you want to spend - cheap folding rigid panels off ebay up to the new high tech 'soft' panels that also fold or roll up, they can be $500+ for an 80w and go up to at least 120w. Like these:
NEW GP 12V 80W Folding Solar Panel KIT Camping Power Generator Portable Battery | eBay
80W Solar Panel Folding KIT Caravan Camping Power 80 Watt Mono Charging KIT | eBay
120W Portable Folding Mono Solar Panel Blanket 10A Regulator Waterproof 5kg | eBay