What kind of inverter/charger do you have on a gasoline motor home? If you have the Xantrex 458 Freedom inverter/charger it should charge all three batteries with no problem. The only thing is that some coaches the inverter/charger is only hooked up to charge the house batteries. Not sure how yours is. The Xantrex 458 comes in 1000 Watt, 2000 and 3000 watt.
As far as buying a battery for the chassis, I bought two to crank up the Caterpillar engine at Napas. They were sealed commercial heavy duty batteries, and they have been real good through the first three years. Had Interstate before and they were not very good. The thing is that the Napa batteries also cost a lot less then the Interstate. I think they are all manufactured by Johnson, then they just slap a sticker on them for different companies. LOL!