Most automotive alternators will not put out anything like their rated current for more than a few minutes. Older ones would burn up, newer ones just derate. Something marked 130 amps might do 60 or 70 after it gets warm.
The small pop up camper will have at most a 15 amp battery charger, this will draw less that 3 amps on 110V, requiring something like 30 amps from a reasonably efficient inverter. The charger may not be putting out as much current into the camper battery as it does on a house plug though - many are not very efficient if running from a "modified square wave" inverter vs. a "true sine wave" inverter.
The biggest problem with charging the camper battery this way is the truck will need to be run a very long time to charge the camper battery fully. If you are going to keep this thing, put 100 or 200 watts of solar on the roof.