I don’t think this will work..somebody will correct me if I’m wrong, but I believe the Mavic car charger requires about 12.5-13v or it turns itself off, that’s why you need the engine running to provide the additional voltage.
As soon as the voltage drops, the charger turns off.
If you just have a ‘static’ rechargeable battery, not connected to your vehicle it will only put out 12v, not enough to keep the charger awake.
Better to maybe invest the money in extra MP batteries, and possibly an inverter so you can plug it into your car and use the mains charger to charge 4 batteries.