RE: How big of a generator do I need ?
I might be missing something, but if you are using an inverter, to convert DC to AC so you can plug in a charger and convert AC to DC there might be a better way to go. Are you using a dedicated 12volt battery to run the inverter? A 1000 watt inverter running near capacity will bang your battery pretty hard, in the vicinity of 80 amps. Also, the inverters that have a stepped square wave output are not clean power. Chargers that run on AC house current usually have a transformer as the load to mains and as such will be an inductive load. the transformers(inductors) are designed to to be powered by a true sign wave as seen in our home. The flat top of the square wave is DC until it for practical purposes immediately switches to a different DC level. They result in a very noisy signal out of a transformer. That is why true sign wave inverters are better for electronics, and they cost more because they are harder to engineer and build. If you are using a big inverter connected to your car's 12volt system, you are going to really be working it hard. Car batteries are not designed for sustained high current loads, they are designed for short term high current loads as seen when starting the car.
But if you are using a 12 volt battery to provide your power to charge your batteries, why not use a charger powered by a 12 volt DC source and get the cleanest power available. this takes the inverting circuitry, transformer, rectifier and filter circuits out of the equation. I should note that there are switching power supplies that don't use transformers, but they are noisier still and probably not seen in these applications. could be wrong on that.
Generators are nice to have and I would not be opposed to having one for my charging but cost and maintenance would be a consideration. Cost especially when clean power is important to you.
I'd be inclined to use a 12volt deep cycle to power a quality dc field charger of sufficient capacity for your needs. Middle of the road deep cycles that I looked at claim 75amps continuous for 45 minutes, 25 amps continuous for 205minutes. So a field charger drawing 8 amps or so and used intermittently should easily last you the weekend with power to spare.
But I'm new here and like I said, I might be missing something.