It's hard, it's even harder when they are killing your chickuns, so it's a life for another. I had to kill a snake, I hesitated for a second, because I didn't want to, but I had to, it had already killed a chicken and was just trying to kill the second. Likewise with an oppossum. In my case I've erred on the side of security, which has worked so far. I wouldn't want to harm the iguanas, they live next to us and they are nice neighbours. So I jam the little chicks in a safe room for most of the day. There are also hawks, and there is no way I can hit them.
I also like to keep diversity as much as I can. I reason that chickens, well, they come from southeast asia, maybe that's why they don't really make it here, as they did not evolve in this ecological context. Of course, neither did oranges, bananas, and most of what are now considered staple "crops" of this region. I've been wanting to write something on the "cosmopolite ecology" that we have brought about.
So I make a compromise, and let the chickens have their man-made coop, because they were domesticated thousands of years ago anyway. And I let them have a little patio of their own, with all sort of alien plants, and they get visited by the local birds (who like to eat their leftovers), and sometimes they get to go outside and enjoy the rest of the place for a few hours before the sun sets.
I mostly struggle with killing the chickens, or the ducks. Well, I don't, but at some point I may need to. I'm waiting for a couple of young males to grow to displace the rooster, but the notion of killing him is something I can't quite stomach. Likewise with the ducks, the whole point was to have duck to eat. I used to take them to the neighbour but I only ended up spending more money than the worth of the meat I get.