Most* Motorhomes will charge all batteries when on shore power or generator power or engine running. There are several different scenarios of equipment and lots of different problems have been conquered to achieve success. Many folks have had mis-wired setups from the factory.
Do some checking with a meter to see the voltage levels before and after plugging in or running the genny or the engine. Some units have a wait time before charging begins, so give it a minute before taking a reading.
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