if the two 12 volt batteries are the ones that came with your rig they may have about 100 amp hours between them of usable capacity. I am not too sure about the TV altenator being able to keep up with the draw on the batteries. I would recommend using 4 6V deep cycle batteries. Hook two each in series to produc e 12vdc and then connect those two strings in parallell to double the available amp hour capacity.
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SOB
2015 Volvo VNL780 D13, iShift, 32k ET air hitch, Idle Free LiFePO4 APU
16.8KWhr LiFePO4, 2.52 kw solar, 10kva Victron split phase
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