Depending on the type of split charge relay you have on the vans, you may be able to wire a small inverter directly into it, bypassing a cigarette lighter socket.
Some of them have a couple of terminals. The TECM units have 3, 1 for the leisure battery, 1 straight through so is live from the van battery at all times and the 3rd is another switchable terminal, usually for a fridge, so again will only work when the engine is running.
I believe the Gardiners charger is an intelligent type so will go to maintenance charging once the backpack battery is full. Alex will confirm.