Guys, Flipacase lives in a CITY. Shooting it is probably out of the question legally speaking, poison also is asking for trouble, too many pets, strays or even kids, live trap and calling wildlife or dog warden is really the only sane option unless there like some cities they do make you need to call a "Pest Removal" company which does get expensive, but not all.
If that truly is the only option, I'd trap it and then deal with it after dark. If you DO relocate it, take it FAR far away, though I do NOT really condone that. Find someone out-side the city limits who can and will humanly dispatch it quickly is what I'd do. A .22 caliber is too small to do it right, I've seen that done poorly. This is a very hard thing to do, but it sounds like you're already working on getting your coop more secure and the run more predator proof which may be enough.
I had a close friend who was a game warden, and while raccoons can and do catch and carry rabies, it's not true that the all have it, and young raccoons are a lot like the young of any species, they don't 'follow the rules'. Again, maybe it is sick, but if they get disturbed by a dog or something chases them out of their resting spot during the day, they'll start exploring... assumptions are not good. Don't assume it isn't sick, take care as if it could well be, but don't panic either.