Personally I would have put a bit of screaming hot lead right at a couple thousand feet per second between its eyes without a second thought. (Sorry if that sounds a bit crude I'm tired, at the station aka work and for some reason online rather than going to bed.......)
Raccoon and coyote are the only 2 critters I take that stance on. I understand they are one of God's creatures and they have their place, but they are extremely adaptable and opportunistic and I think in certain situations they need a little pressure pushing back on them to keep them in check.
But unfortunately many folks don't agree with that opinion and judging by the OP's comments I got that impression. I was trying to make the most of a bad situation. I don't agree with relocating them however I'd hate to see someone go through the effort, release their chickens back into the yard (assuming the problem was addressed and now safe) and then lose their birds because it was back in less than 48hrs and killed everything in the yard.
Sorry I wasn't clear on that. Don't worry Thistle we're good!