I hear that! We have one that leaves tracks in the snow at our home, but we never see it during the day. Coyotes were a real problem in our area a few years back killing off pets and all the small animals.
My wife used to train dogs and one of her students had a little chihuahua that was carried away by a coyote. They also have an interesting way of using a female coyote to lure out a domesticated dog then they attack.
Oh no! That is so sad to hear, she must have been devastated to see that happen. We don't let Mika out at night without being on a long leash, just in case one comes into the yard now that we know there is one out there in the woods behind our house.