Battery tenders from Deltran are a great product. They are used just about everywhere there are batteries - marine, trailers, cars, motorcycles, etc. There are a number of Battery Tender models that can handle one or multiple batteries. Chargers
Keeping the chassis battery in the coach on a Battery Tender is a good idea as the battery will keep the memory in the engine computer, and the radio memory.
I think the above posters have it about right. Remove coach batteries from coach or trailer, clean them up if needed, top off with distilled water, and store in the home basement with the Battery Tender.