Skunks are easy to live trap. Bait with peanut butter and then shoot it while it is in the trap. Make sure you are upwind for killing it. And place the trap where the skunks will find it but you can safely shoot it once trapped. You probably will find there is more than one. I routinely killed a dozen each and every year. They repopulate rapidly.
Add some electric wire around the outside of your pens too.
Add some electric wire around the outside of your pens too.