First, I would recommend that you not use your frig on 12v it draws to many amps. Just use the LP, you should have no problems driving with the LP
For my unit, due to wind flow, my unit works better on 12V than LP at highway speeds. So on days I'm making infrequent stops, I use 12V. Even with the 10amp draw of the fridge, I can still charge the coach batteries at 20A/hr. I just pulled a 2 gauge wire from the vehicle battery to a heavy duty connector for the battery lines to the camper.
If you don't have a heavy enough cable to provide the recharge and frig, then suggest you use propane for the lp. I use LP on days when my interstate driving is limited. Below 52mph, my fridge works just as well on LP as battery.
I don't see how a battery-battery charger is going to help you out, since you will still need to charge the source battery. And if the source battery is the truck battery, you will still need to upgrade the wiring between the truck and camper.