If the gennie has been sitting for a spell, and nobody has run it regularly, it may need some work. I was supposed to run mine once a month for 30 minutes under a load, to keep it working properly. It may be idling fine, but can't get the fuel it needs to operate under a load.
To see if it is the gennie, and not the water heater, you could start the generator with the Heater off, and then turn the fridge on, and plug in a shop vac to one of the inside outlets and turn it on. That would create an immediate load on the gennie. If the gennie handles that, then it may be the element in the water heater causing a short.
If the water heater has water in it, and the element is fine, then you'll probably have to take it somewhere, and have it looked at. A decent small engine shop that works on gennies, or your local RV dealership. We have a really good generator shop here in Pensacola, that works on a lot of RV gennies.
Sorry to give you the bum steer yesterday. I didn't realize they had them set up to where you had to plug the camper into the gennie.