Mounts loose maybe
Are the mounts where the generator mounts to the frame loose or maybe missing. It is not unusual for the generator to bog down a bit when putting it under heavy Load, but there should be no vibration. May be a govenor problem. how long do you run it before starting the ac? has the generator stabilized and warmed up before putting it under load. If it hasn't been run for a long time or you have stale fuel in the tank if gasoline driven, then you might add a bottle of Sea Foam to clean the fuel system. If you can't solve the problem, Take it to a Onan Depot for service. Well worth the time and money and they have the proper test equipment to test everything. They could find any problems in 10 or 15 minutes. to many RV dealers don't have the experience to do proper work on them and most are parts changers.
2006 Four Winds Hurricane 31D, Steer Safe, CHF, 50 Amp Conversion, 3000 Watt Inverter, Toad is a 2007 Jeep Liberty Sport. Blue Ox Aladdin Tow Bar, Apollo Braking System