That's a tough one. Normal wiring diagram should show both the generator and the shore power line connected only to the load center. So the AC should work regardless of whether the power source was generator or power line.
Do you have two ACs, and one works but the other doesn't when connected to shore power? If that's the case, then shore power must be a properly wired 50-amp plug in order for both ACs to run at the same time. With a 30-amp plug, only one AC will work.
Keep us informed as you figure it out.
Grumpy ole man with over 50 years towing experience. Now my heaviest trailer is a 7,000-pound enclosed cargo trailer, RV is a 5,600 pound Skyline Nomad Joey 196S, and my tow vehicle is a 2012 F-150 EcoBoost SuperCrew.