When the AC is on and the car idling in the driveway, you loose all the coolant in the radiator in 10 minutes? You’d think there’d either be lots of steam in the engine compartment or coolant leaking on the ground under the car when that happens. Do you see either?
Remember that the overflow tank could be empty but the radiator is still full. Are you checking the overflow tank (a plastic bottle usually off to the side of the radiator) or the radiator itself?
When the engine overheats, how are you making this determination? By a dash coolant temp gauge? Or some other way?
When it overheats, are the radiator fans (in the engine compartment) spinning like banshees? They should be.