Hi,
If you plan on making coffee, and blow drying the hair, do one at a time, as each can use about 13 amps. The charger on board the RV is more powerful than the tiny attachment on the generator, that is only rated at 3-6 amps. The RV generator is 35 - 45 amps, perhaps 65 amps?
Plan on running the generator about 1 hour per day, and that should keep the battery full enough to run the pump and some lights.
If you want to run the laptop computer, or charge cell phones, or some other small loads from the 12 volt battery, then you will need a small inverter. It changes 12 VDC into 120 VAC. Yet you can not run large loads from the inverter, as a coffee maker will draw 150 amps at 12 VDC and quickly discharge the battery. It is fine for a 5 watt cell charger or 20 watt computer, even a 75 watt flat screen TV. But not the larger loads unless you have a lot of batteries.
I bought a inverter at Costco, rated at 500 watts and it plugs into a cigarette lighter. Anything between 150 and 500 watts should work fine. Larger than 500 watts, and the start up amperage and run amperage (even without a load) will be higher than a couple of batteries can support. Make sure that you unplug the inverter when not needed, so that the battery will not be dead in the morning. Also charge the cell phones as much as possible while the generator is on, or just before starting the generator.
Have fun camping!
Fred.