I have a pigeon nest that has been here for two years, how do i get rid of it?

So we just moved in to our house two years ago. When we moved in we noticed a pigeon nest on the side of our house above our water spout. We did not think anything of it but now, it is to the point where I cant stand the nest any more. The crap all over our faucet knob to turn on the water hose and are constantly cooing. We heard that once a pigeon makes their nest, they wont ever leave. That they will return to it for the rest of their lives, and to get rid of the nest during the winter is to be basically killing them. Is this true? I DONT want to be inhumane about getting rid of the nest, I just want it gone. I dont want to hurt or kill them so what should I do? How do I get rid of this nest as humanely as possible?