The theory sounds workable to me, in general. I might think about rejiggering the battery isolator system so that the house and chassis batteries are not tied together while the engine is running, though that's probably not essential. I'd also make sure that the new alternator is rated for continuous heavy-duty use; many are really only designed for intermittent heavy loading, and that's not what you're proposing.
Do make certain the regulator sense wires are connected to the batteries that the respective alternator outputs are going to. It would not be good to have the alternator sensing the chassis voltage while powering the house system.
"Proper wire gauge" is going to be quite heavy.
