You just answered your question as to why your alternator is constantly charging, The coach battery (or batteries) are shot. If your motorhome doesn't have a battery isolator you need to get one. I had chassis/coach batteries in 4 different tool trucks in 28 years of the tool business. @ trucks had isolators and 2 used a constant duty relay to charge the coach batteries. The isolator separates the 2 electrical systems and only charges the batteries that need the charge. Your engine start/chassis battery doesn't need much charge unless you are using the lights, heater, wipers, etc. If you use the camper for any length of time those batteries will need charged. With no isolator your system will charge one set and overcharge the other set. I had many battery and alternator failures because of overcharging in the trucks without a isolator.That bad coach battery will cause the system to overwork.