The least use of gas and the safest way to use your car as a house battery charging system would be to do this with jumper cables while the vehicle is parked.
An alternative would be to string some 10 ga. wire from the chassis battery and connect to the house batteries while traveling.
I would suggest to use one of the magnetic solenoid type relays for battery isolation. One like
this. I wouldn't get too hung up on different charging voltages with AGM vs FLA batteries. I have both interconnected in two banks and one solar controller feeding both banks. All the batteries are doing fine after more than a year being interconnected. I tend to set my charging voltages on the high end of acceptability since most battery MFG's try to CTA with charging profiles, choosing to derate charge amperage and voltage, thereby selling more batteries.
I've found that my AGM's will take most anything I throw at them as long as voltage isn't above 15VDC.