Shooting him was the best thing you could have done.
Poor thing shouldn't have had to deal with that snare in the first place but you were humane and rational.
Hardest thing I've ever done was kill a Canadian Goose. It has been hit by a truck and was lying on the side of the road. I went over to get it - I wanted the wings for a taxidermy project - and then realized it was still alive. After calling all the local (and not so local) humane societys and vet clinics I was told that the soonest someone could be there would be 4h. It was clearly suffering and I didn't want to leave it there in pain, bleeding to death.
So I took out my axe, something all females should carry, and put the poor thing out of it's pain.
One of the most emotionally testing things I've ever done but no regrets. Just lots of nightmares about geese.
Eep.
Coyotes are very good at causing destruction and not much else. They tend to kill everything that they can sink their teeth into, so it's good that you killed it. If you didn't bury it yet, I'd consider taxidermy... It'd make a nice mount. btw, congrats on using the 2nd ammendment for protection!
Everyone has been very nice about this, I expected A LOT more negativity.
I went out this morning before work and cut off the snare and buried it.
My wife agreed, we're giving away our last few hens. I don't want to be locked in a cage, they have been free-ranged their whole lives.
On the brighter side, we're getting our goats back (they've been out on loan for a year). Coyotes don't mess with them, the buck weighs about 200 pounds and has 18" long horns!