Not sure about that. i would think that the charger that comes with the trolley is an intelligent trickle charger. Putting the charging system of your van straight into it could fry it as the van charges back into its normal battery at up to 14volts.
I don't know enough about batteries to advise further. perhaps someone could.
Andy
It's not the voltage that's the problem (12v), its the amps that a vehicle's alternator charges at that will fry it. You should be able to get a 12v charger which is designed for purpose, as a charger is for a mobile phone etc. Again it will take ages to charge, so probably will not help solve your problem.
Our backpack can take all night to charge when the battery is flat, so this would take as long if charging from the vanthrough a 12v charger.
Spruce