Trapping and relocating was just what DH and I were talking about in regard to a very big, well fed woodchuck eating my garden; I was talking fencing, my youngster suggested moving him to a new home. DH had to explain the problems with moving a wild creature and it's against the law. He was a wildlife management major in college. THere are many good sound reasons why wildlife cannot be rehomed which is why the law is written the way it is; rehoming is good beneficial to us and gets rid of our problem, but it is not always good for the animals and their well being.
As for crows, we keep an old tree that died so the crows have a perch; we welcome the crows because they keep the hawks out of our area; plenty of hunting space for them in the preserves next to us. I expect to loose a bird or two, it goes with the territory; I love the wild animals, too and try to find a compromise. My dogs usually keep the coyotes moving along too. THis section of the woods belongs to my dogs and the coyotes know it; the coyotes pass thru on the deer trails very quietly. As long as they keep going and don't eat my chickens and sheep; if they do, time for more fencing. IT's a compromise. I live in an area where so many houses are going up and woods are being taken away from the wild animals, where are they to go? I have plenty of gray squirrels--happy to share some of those! And that wood chuck could feed a whole coyote family! DH said they taste awefull--I was thinking dinner!