We have raccoons, possum, foxes, bobcats, weasels, dumped dogs, dumped cats, neighbors dogs, red tailed hawks, bald eagles, owls, a rare black bear or two now and then, AND thick as thieves COYOTES coming out of our ears.
Sounds like our predator problems are similar, minus the big cats. Was surprised to learn of a bobcat killed by a car just a couple of miles from the house last year. Black bear are very rare here, but there have been confirmed sightings in the county. I would almost rather deal with big cats and black bears than dang weasels. A weasel will get in a hole no bigger than a mouse hole and wreak havoc. Red tail hawks are everywhere here, and bald eagles are making a strong come back. I have seen them myself several times. Last year I killed 14 'coons around the chicken coop. The population wasn't even dented, as they are back in force already. I'll be setting the traps again this weekend.
Strange that the coyotes attacked dogs. I grew up in deep south Texas where coyotes are a common as chicken in a Chinese restaurant. I've come up on packs and ran them off with a stick. Unless the dog gives pursuit and challenges them, they would rather not fight. In fact, they wouldn't even take down a steer. They had a brilliant way of cutting one out, then running it over an arroyo to its death. I found many cattle skulls in the bottom of arroyos and sold them to the winter Texans as a kid. I had my dog with me many times (pit bull/akita) and the coyotes had no interest in tangling. They just wanted to be away.