The front coil is called the evaporator coil and the back coil is the condenser coil. The air in the RV is pulled through the evaporator coil and heat is pulled from the air and then cool air is returned to the RV. Are you sure you have checked the tray below the evaporator coil and know for sure that the drain holes are clear.
You should be able to pour a quart or two of water onto the top of the evaporator coil and see it run down the evaporator, then out the drain holes and then on to the roof. If the evaporator drain pan fills up with water, it then overflows and water drips out of the ceiling assembly and into the RV.