As said, the 2000 watt Honda will nor reliably run your AC. But if you are ok with that the 2000 watt Honda is an excellent choice. Consider that a higher output generator will be quite heavy so loading/unloading and carrying it around becomes more of an issue.
Another thing to consider if your main intent is to keep your batteries charged: Many OEM converter/chargers do not work as advertized. The WFCO models that are very common in trailers are notorious for not going into boost mode. Mine is one of them. Using just the WFCO OEM converter/charger takes an extreemely long time to recharge the battery (like days). You may have to get a portable smart charger or replace the OEM converter/charger in your trailer to keep your battery charged using a generator during the limited times that most campgrounds allow their use.