I am NOT insane. I would NOT be pleased if the situation that you desrcibed occured anywhere, even in your backyard. You, however, are, rude and reactionary that has probably never lived in the country for any length of time. Coyotes do a great service of keeping the other wild animal population in check. You DO NOT eradicate them. You learn to live around them. If you relocate them to a non-populated area, what is the problem.
I live in a semi-rural area. One that until very recently was quite rural, but is being encroached upon by new housing developments. There is still rural area not so far away.
New Jersey, however, is highly populated. Where could they be relocated to?
What has happened is that as the hunting population in the US has declined, all manner of wild game has returned with a vengence. This brings back the preditors.