In my little old motorhome, I had to warm up the generator before I could turn on the AC. This typically took about 3 minutes, then I could turn on the AC and have super cold air. That was in my Class C with a 4KW generator.
Typically when one starts a generator, everything plugged in and turned on, including the battery charger, is fighting for the power. I would turn everything off before starting the generator (flip off my breakers) let the generator warm up then start turning things on. If AC was a priority then naturally... I turned it on first and got it super happy and cooling before adding more stuff to the load.
This spring I traveled in a camper van with a 2kw generator and it would run the AC if we switched the fridge to propane AND waited about 5-7 minutes for the generator to warm up. No idea why we had to wait (I am not a techno guru) but that is how we learned to work it, so we were plenty happy. I speculate that the battery charger was hogging the generator for that first 5-7 minutes and once it settled down, the AC was happy.
Once the AC was running and the place cooled down, we could usually switch the fridge back to electric (if we remembered!) and both would run off the 2kw.
I think it had something to do with the AC and fridge both needing extra "starting" power as opposed to "running" power.
I just used my ears to listen to the generator, as I could tell from listening to it, when it was warmed up and happy. My friend thought I was psychic, cause he couldn't really hear the differences I was hearing.
Somebody with techno expertise can probably explain all this a lot better... ;D