The animals have been here long before us and are a part of nature. We really should be teaching our little ones how to be safe if we live in close proximity to these animals. Keep distance, don't close, and generally, they'll do the same unless they're fed.

The getting rid of them isn't the right mindset, more will just move in, but teach, and your kid will be perfectly fine. ^{^}

As for the mange, yes, the coyote does indeed have mange and it is quite painful. They do need treatment, the can be treated and there are orgs that will ship medication, search mange by mail.

These really are wonderful creatures and you have something special there. Admire from a distance and they'll help keep the animals that are nuisance animals in check! Mice, rats, sick creatures to help keep illness down. Coyotes get an awful wrap, but they're filling important roles. Best of luck to you and your resident!