When plugged into any AC source (either shore power or a generator) your 12 volt is usually supplied by the battery charger/converter. The charger/converter converts 120 volts AC to 12 volts DC and charges your battery. When not plugged in to any AC source your 12 volt DC is supplied by the battery only. With 1 Honda EU2200i you have 2200 watts max output, 1800 W continuous. These outputs are rated at sea level and decrease approx 3.5% per 1000 ft. You do not mention the size of your air cond, it is either a 13,000 BTU or an 11,000. It is most likely a 13,000 unless you have a small trailer. It could be a 15,000 but these are usually only found on a 50 Amp trailer. Most users are concerned about in running an air conditioner when boondocking in hot weather. If you install an EasyStart on the air conditioner, and disconnect the battery charger/converter while running the air cond you can run the 13.5K air cond on one EU2200i and it may also be able to run on ECO mode. You won't be able to run any other 120 appliances while running that air cond. Investigate the wattage your microwave to find out what it draws. You have to manage your usage. Another option if you decide you need 2 EU2200i's is that you can get 2 standard units and get a parallel cable to join them together. You need to do some research to become familiar with all options. Hopefully this help further your RV education. It took me a while to figure much of it out and every day brings new opportunities to learn more.
good luck.