I'd think a raccoon could have taken out those rabbits way before a fox. The raccoons I've seen around here are BIGGER than the foxes, for one thing. Add in the dexterity and intelligence and you've got a major predator.
I'm wondering if your recent attack was maybe a juvenile trying to hunt on his own, maybe that's why you didn't lose birds? I'd try a live trap and see what you get. But, with a live trap, you have to be prepared to kill what you catch. Relocating it won't work, I don't care how far you drive. Sounds like hardening the coop is already on the way, no?