We are staying in a campground that has no hookups, therefore we are having to run on our batteries. We have an 09 40' Phaeton with a commercial frig with 6 house batteries. No problem with charging...
It is big enough but something in your coach does not play well with the Honda.
I have seen this issue but did not get to pursue the resolution. Something with the ground etc. Not much help but the 2000 is plenty to charge things. You need to turn AC's off of course and put the HWH on propane to keep the load down.