You can use an 3000W inverter to power the A/C, but in your case you will have to rewire lots of things:
- The panel to run the A/C from the inverter
- Most likely the A/C wiring to and from the inverter to the panel (needs to be 10AWG for a 3000W inverter)
- The DC wiring from the batteries to the inverter and potentially between the batteries for the higher power inverter (DC wiring must handle 300A as nothermark mentioned).
As stated above plan not to use more than 50% of your lead acid battery capacity. This limits the amount of time you'll be able to power the A/C, less than 1.5 hr in the example twinboat mentioned.
Also you will need a good quality 3000W inverter with high surge capability, I would use only Pure Sine wave types to run large appliances such as A/C's.
We successfully run our A/C on both the coaches in our sig below, however I designed the systems to do that. Also, like the Wynns and others I use LiFePO4 batteries. I started with about 1000AH of Lead Acid in the Newmar, but they only lasted a few years, probably because I bought cheap ones.
For solar panels, if you simply want to keep the batteries charged while stored you'll need much less than if you want to use them while dry camping. There are lots of threads on this forum and lots of guides on the internet, I'd investigate some of them to get an idea of what is possible.