Is your inverter tied directly into the same panel as the shore power? Is it 30A or 50A? If 50A, one of the ACs is typically tied to one side of the 50, and the other AC (as well as the rest of the RV) is tied to the other leg. If your inverter setup is tied to only one "leg" of the incoming shore power, you already have the problem solved.
BamaDuke
KC5NCZ