I don't know how old your kids are, but I would keep them inside too. A kid a few counties over from me was playing in the backyard and was dragged off by a coyote a couple years ago.
http://losangeles.cbslocal.com/2013/07/23/toddler-recovering-after-coyote-attack-at-oc-cemetery/ this wasn't the same incident, but young kids are definitely in danger of coyotes. More likely than not though, yotes will only attack a human if they are in a large pack, seriously desperate or if the human looks like it can be taken by said coyote. It may be a small chance, but the chance is still there. I would do the same thing.
not to mention the diseases a lot of them carry..
And I agree with above posters, I would get a gun to shoot it with and use a distressed rabbit call to call it in. I've heard from quite a few sources that if you kill a packs member and hang the body from a tree where the pack will see it, they will move on from the area. I haven't field tested it myself though. Good luck!
http://losangeles.cbslocal.com/2013/07/23/toddler-recovering-after-coyote-attack-at-oc-cemetery/ this wasn't the same incident, but young kids are definitely in danger of coyotes. More likely than not though, yotes will only attack a human if they are in a large pack, seriously desperate or if the human looks like it can be taken by said coyote. It may be a small chance, but the chance is still there. I would do the same thing.

And I agree with above posters, I would get a gun to shoot it with and use a distressed rabbit call to call it in. I've heard from quite a few sources that if you kill a packs member and hang the body from a tree where the pack will see it, they will move on from the area. I haven't field tested it myself though. Good luck!