I would use the weaker one first. You will have a good idea how long the better one will last then.
With your voltmeter, and when you are not using loads for 30 minutes or so (like pumps or fridges or lights), measure and record the battery voltage and hours used. It's very useful to have a chart and then you will be able to judge how long it will take to use up each .1 of a volt. I use up about .15 from two 6V batteries each day, so get 4 days from 12.6 to 12.0
Plug your camper into the generator through a 15 Amp dogleg, and let the converter charge the battery.