It's fairly common for raccoons to be out during the day. Especially females with babies.
You absolutely have the right to kill an animal that is endangering your livestock. It wouldn't hurt to have a predator proof run as well though. Like others said, another predator will eventually take its place. Easier to be proactive than reactive.
I have a run that's fully enclosed with hardware cloth, which sits inside an "open" run like yours. I like that they can safely be outside if I'm not home, or if we've had predator sightings.
Do you have a dog? They make it much more difficult for predators to sneak around during the day. My dog would gladly kill my chickens (hence the fenced open run instead of free ranging), but she's also very happy to chase any other animals who get too close.