Battery issue

My coach will charge the house battery from the engine, but shore power won't charge the chassis battery. Found that out when we went on our first week-long trip a couple years ago. I usually run the dash radio (powered from the chassis battery) all day to keep our dog's hearing entertained (otherwise known as keeping him from hearing everything in the campground and barking at it until we get evicted) when we're not with him. Although the radio kept playing all week, the engine wouldn't turn over when we got ready to leave...had to use the boost feature...glad I had that! To remedy that situation, I installed a Battery Tender trickle charger that is connected to the chassis battery and works when plugged in to shore power or on generator. The Battery Tender itself is plugged into the old TV outlet in the dash that is defeated when the engine is running, so the Tender is not trying to charge in addition to the alternator. Been working great for 2 years now!