It sounds like your coach does not have inverter by-pass switches. If it does, you should be able to use them.

If your house battery voltage is too low your inverters will not power up. Your symptoms suggest thids may be your problem. By starting your engine you are able to get enough charge on the batteried for the inverter/chargers to pass AC power. Where your inverters dead before starting the engine? If they were, where you dry camping and running on your inverters? What error are your inverters reporting?

If you need batteries you shouldn't have too much trouble finding a good RV shop or renewable energy shop that can replace your batteries. I would also think WW Williams in Vegas could do the job. In a quick Google search, I'd call this shop. They say they do battery exchange and inverter work.

http://www.happyhalsmobilerv.com/services/