Running the gas furnace does not cause moisture in the RV. The heating by the furnace is a straight adiabatic heating and the number of grains in the air is unchanged.
The solution is to limit and control moisture in the RV. Keep a roof vent open about 1/2", maybe two open a bit and one window cracked open just a bit.
When cooking, run a vent fan to get the moisture out of the RV. Also, the open flame puts some moisture in the air.
When showering, open the roof vent nearest tot he shower 2" or 3" and when completed, run the vent fan for a minute or so. Also wipe down the shower with a squeegee to get the extra water out of the RV.
Next RV you get, order the Thermo pane or dual pane windows to reduce the condensation problem.
A dehumidifier is not really the answer. You can pretty much make your own part time dehumidifier by running an electric heater on low and run the A/C unit. This is all a dehumidifier does, but it used the hear from the condenser to heat the air.
Ken