Running air conditioner off solar and batteries

We have a 2004 Interstate. We've added an extra house battery to power astrophotography equipment and a solar panel to charge both batteries (house and extra). We try to camp where it's cool at night but occasionally we need the AC. It isn't too noisy when we have shore power but it is too loud to sleep if we have to run the generator. Has anyone else tried using batteries/solar to run the AC? We took the microwave out which is the only other big energy hog.