What's the load like on the genset? With mine, when I start it up it goes into bulk charge mode for a couple of minutes which really reduces the available output. I usually wait until the current draw from the batteries goes down before switching on the AC - and also make sure that I don't have the electric water heater on when the compressor is starting.
Everything will play nice together if I pay attention to how I introduce the loads onto the genset.
If I don't do it right, breakers will trip and I have to do it over.