i think you're confusing "inverter" with "converter".
all RV's have converters, that convert 110v AC power to 12v DC power. it also recharges the battery when connected to shore power.
some RV's, especially motorhomes have inverters. these do the opposite, inverting 12v DC to 110v AC, so that you can run things like a tv, dvd player, air pump, razor and so on. as long as it doesn't draw too much power from the batteries.
with a popup, you can add an inverter if you want. i'm adding one to my HTT, since we almost always dry camp.
if you never dry camp, there's no need for an inverter.
a generator takes the place of shore power.
"Inverter" generators, like the Honda or Yamaha 2000w, provide clean power for delicate electronics.
a generator will also use the trailer's converter to recharge the battery. no need for a separate charger or 12v charging wires.
Inverter generators are also MUCH quieter than open-framed construction generators, along with providing cleaner power. but that costs more.
finally, if you want to run the a/c, then you'll need enough wattage to power it. so a 2400w generator would be the minimum.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC