First of all, your camper should have only ONE AC-Voltage input connector which would power everything that runs on AC-Voltage.
If your camper has two AC-Voltage input connectors then it's wiring has been modified, which leaves me without any idea what your problem might be.
I can say that with a standard wiring in your camper, your system would have been designed to handle the load of your AC unit as well as your other appliances. And, in addition, your interior lights, your alarms, and some other accessories would be powered by your COACH battery and the battery would be kept charged by your built-in Converter which itself runs on 110-VAC.
I would need more information on your camper to make any further assumptions.