I don't understand why people believe that relocation is ever an option. Study after study has proven that if you don't take them far enough, they will be back the next day. If you do go far enough, say 20 miles at least, you are dumping an animal that is not familiar with the territory into territory that is undoubtedly inhabited by members of it's own species that do. Foxes will kill strange foxes, as well as predators do. Foxes that don't know the lay of the land will starve in territory where the resident foxes have claim on all of the food resources. It's a question of killing it slow, versus fast. Relocation is either a minor inconvenience or a death sentence, depending on how far you go.
Then there is the matter of disease transmission, an animal willing to enter a trap could be hungry because of disease. You could be infecting all of the animals at the release site, who no doubt will come in contact as they gather to kill the starving interloper.
And there is the ethical question of taking an animal habituated to human food sources to the point of becoming a nuisance to someone else's house. To be somebody else's problem. How kind. Never relocate. Most wildlife agencies either have laws against it, or will soon, as they become enlightened to the potentially devastating impacts it can have.
Human safety is also a concern. A younger animal might be hungry enough to eat chickens because it's parents died. Maybe the parents died of rabies. Maybe they infected the juvenile. Maybe it bites you when you release it, or maybe you scratch yourself on the cage that has blood and saliva on it from the animal biting the wire. Ever catch rabies? Few people can answer that question with an intelligible answer. If you get exposed, the treatment is costly, but if you get infected it is fatal. Rabies is just the tip of the iceberg, there are a host of other diseases you can pick up from wildlife. Sometimes, they don't prance through the field of flowers when released, they run straight for the nearest cover, which is probably your vehicle. Don't leave the door open. Usually it's wheel well and then either on top of the gas tank or in the engine compartment. Fun times.