Welcome to the Forum.
I suspect your talking about a "converter", not an inverter. The Converter is the box that makes 12 volts when your plugged into shore power.
I recently replaced the converter in my 99 Southwiind. I was dealing with other issues and wrote an article on it. However, If you scroll down near the bottom, you'll see the inverter I chose to replace my old one.
Coach 12 volt power upgrades – 1999 Southwind 35S
I'm not understanding what you are saying about your A/C units.. If you look on my site under the DOWNLOADS tab, you will find a lot of manuals that may also apply to your Southwind. This link is to the ECC control and tells you how it works.