Best guess, with the batteries "ON" you have sufficient amperage available to run the jacks. With the battery switch "OFF" the shore power is trying to supply the necessary 12 volts but the converter does not have sufficient capacity to supply the necessary amperage.
You should definitely be ON to run the jacks!
With that kind of budget, I would be buying a good tent and camping equipment, then renting or buying a SUV. Even $5000 won't buy much in the way of a reliable SUV.