yours is the classic case of putting the chiller pump at the wrong compartment. If you place the chiller pump in the return pump compartment and the chiller return at the same compartment, you chiller will not work correctly....why? because the cold water will be pump again into the chiller and the thermostat will sense that the temp is cold and will cut off.
So its like circulating within the return pump compartment and very little cold water will be release to the main tank.
U should change the position of the chiller pump to another compartment (for your case is your skimmer) and the chiller output (cold water) in the return pump compartment. With this, the cold water will be release up to your main tank and not be circulated back to the chiller.....
U try and it should work......one coffee for me