I use a Honda 1000 for the same purpose that you describe.
The 1000 does the job of charging two TC batteries.
Simply plug the camper's shore power plug into the Honda's AC outlet.
(Forget about using it's DC output)
The 1000 is rated at a 9 amp output - so charging batteries will be a little slower than using a Honda 2000 - it means a little more run time to gain a full charge.
But generally, I never get close to depleting the batteries enough to require a heavier charger.
The 1000 fits into storage where the larger 2000 won't fit.
My lower back appreciates the lighter weight 1000.
My camper has a Onan 2400 which I could, but never, use to charge the batteries, it's just not necessary.
That said, the 1000 will barely run a Skill Saw or small chain saw.
If I bind the saw blade at all, or run the chain saw aggressively, it will pop the safety circuit breaker on the 1000. I have to stop work and reset the breaker.
At those time I think the 2000 would have been a better choice.