Are they impossible to catch/trap/shoot?
That's what ate my dear Maple and went after my Luna. I've seen it 3 days in a row. It's huge!
My husband is after it now, but I hate to say my girls will be locked up until the coyote is gone!!!!
I know they are usually solitaire. Buying a live trap that big is a bit spendy. Maybe we can make one that's not a snare. There are too many dogs/cats that can get hurt.
What are our chances of getting this awful predator?
Yes, you can do all three but shooting is by far the easiest and most humane way.
You should see their canines! Twice as big as a shepard's.
They are definitely not solitary in their habits unless they have been kicked out of the pack. Where you see one there are at least six in the woods you can't see.
Have your husband put out the call within his circle of friends, most likely there is a coyote hunter among them and he will be most willing to come over with his gear and put a hurtin on the yote.
As Centrarchid said, it may be a wolf in which case it may be protected by law. I would contact the local wildlife dept. and inquire about nuisance wolves in your area. Sadly, you may have to provide them with photos of dead carcasses and of the wolf in question to get them to act.