AGM’s like the upper food chain Lifeline brand are expensive but worthwhile but if you’re running the generator constantly they’re probably not worth the money. Unless you’re in an all electric coach lead acid batteries should cover your needs overnight until you start the coffee maker or microwave in the morning (unless you have one of the very large inverters). In fact if you’re cooking the batteries your charger is suspect, i.e. may not be going float mode once you get above 13.x volts. This tutorial may help but strongly suggest you have the charger checked (and it’s settings because different charging profiles are used for different battery types).
http://www.chargingchargers.com/tutorials/charging.html