You are missing the Point. To check house batteries take a DC VOLTMETER and probe positive post and minus post of each battery and check the voltage. Then, while cranking the generator check the voltage at each battery-- should be 5 to the 6 range. This assumes the batteries are 6 VDC batteries wired in series and you are checking each individual battery.
Then go with the voltmeter probes one to the plus side of one battery and to the minus on the second battery (you are now checking across the two in-series 6 VDC batteries so nominal voltage is 12 VDC) and crank the generator and the check the voltage-- it should not go below 9 volts.
Also check all cables connections.
If one battery is bad you need to change out both batteries as a PAIR. The old battery will pull down the new battery and you will still have a problem because the internal resistance are different. Do the same on the main motor battery-- should not go below 9volts when cracking. With this method there is no guessing.