Power (charging) problem with pre-owned Host camper

GFCI's are well known to trip when fed from another GFCI
Very complicated reasons as to why they sense a fault but its commonly accepted that you can't feed one from another .
Change to a different plug in the house and it will work just like it does on the genny.
Whoever set this up was likely unaware of the potential problem
You don't find this in a factory or licensed electrician work
Good Luck, Mike