I'm running a 105agm aux battery and a narva 140amp vsr in my TJ. I have also upgraded the charging system from ECU controlled charge rate to external regulator charging system. I run 14.2V from the alternator now and have zero dramas at all with charging both batteries. From my aux battery i run the fridge, all lighting, compressor, oven, 240v invertor, water pump and multiple 12v/usb outlets in the rear.
The vsr waits till the crank battery has reached 13.3v before engaging and charging the aux battery. I've had this setup running for well over a year now and has never failed me.

The only thing to remember with running a vsr is that you will need charge cables running to it the same size or bigger than your standard battery cables. I have tested mine a few times after running the fridge, oven and invertor overnight, when i start the car it takes around 60 seconds for the vsr to kick in and start charging the aux, if i have given the aux battery a flogging overnight then the main charge cables to it have peaked at nearly 90amps for the first few minutes then comes down to around 10-15 amps before gradually settling to around 4 amps for a few hours.