Raccoons are incredibly intelligent, and extremely dextrous with their small tootsies.
Once upon a time, I stole a baby raccoon (eyes weren't even open) from a nest. She grew up to be a wonderful pet, with amazing skills as a "break-in artist". Took her home from college (many thanks to Shakey's Pizza to this day, for warming baby bottles), but she never became a pest with my parents' free-range chickens. Was totally free and followed her people everywhere.
But.....that doesn't mean that Tulip was an "ordinary wild varmint". Unfortunately, many people feed feral animals, helping them to become an absolute nuisance. And many a rural dog has met a formidable opponent with an adult raccoon (these guys can fight viciously , and may).
Never, never relocate any wild animal !!! As others have said, it merely creates problem for someone else, or a return to YOU. Raccoons can often have a high incidence of rabies among the population (in the SE they often carry deadly parasites for horses too). As others have said, releasing from a live trap only serves to make a "trap-wise" animal. Again...raccoons are SMART & adaptable.
In some states (largely because of the possible rabies exposure) a rural USDA office may offer assistance with coons and skunks (also common harbingers of rabies).
Rule No 1: Varmint proof your coop! And don't leave ANY food out for wild critters, including in bird feeders.