How about leave the coyote alone? Second choice, get your mom a can of bear spray, and carry a 38/357.
People let pets out, think of the coyote as providing Darwin's natural selection.
I've got a coyote that we are pretty sure has been eating catfood we leave out for what we think was an abandoned cat, and our visiting skunk. One morning, crows are going crazy, Coyote is bold as brass, jogging straight to our porch, with eyes on it. Crows scared him off. I ran outside with my 300 mm lens, and Nikon, and, tried to take a few pictures. Meanwhile, the crows had warned all the cats, so they were now all on 2nd story perches, and, I followed the coyote. At about 140 yards, I got two pictures. I tried coming out of the bushes, and bracing against a tree, but, as soon as he/she saw me that coyote bounded into the thick stuff, and was gone.
Nature sure is amazing, and the way it works...
How about no? It's following people around and eating pets and a potential human danger. It's an animal, and it's life is of lower value than that of the ones it's threatening. Nature gets a lot less amazing and wonderful when it's stalking your family. It will be shot one way or another. Think of me with a gun as natural selection.