The main difference between and air conditioner and a dehumidifier is that the dehumidifier places the heat that is taken out by the cooling coil and places that heat in the same room. An air conditioner places the heat outdoors. Placing a dehumidifier on an air conditioner is redundant.
A commercial air conditioning system can take humidity out of the air and reheat the air with a heating deck. This is similar to turning on the air conditioner and the heater at the same time. You could turn the air conditioner on and place a heater in the room.
Running a fan all the time will not take out humidity, the moisture has to settle on a cool surface below the 'dew point.' If a well is available, you can sprinkle your lawn and take humidity out on a fan/cooling coil with the ground water running through it; anything to make a cool surface for the moisture in the air to condense on a cold surface.