The tap is a vacuum controlled coolant tap for your heater. With the vacuum line unplugged the tap is shut so that is why your heater doesn't work well.
When you disconnect the vacuum pipe to make the car run better do you plug the pipe? If you do plug it then maybe your coolant tap is leaking the vacuum.
I'd be plugging the vacuum line for the coolant tap and trying to tune it and get it running properly. However with the heater controls on 'cool' the hose should be effectively plugged anyway. Maybe not 100% plugged though and hence it runs better but not perfect?
Whatever is going on I'd be pricing a coolant tap.

