We had this problem several years ago. A vixen set up a den under neighbor's vacation cabin and fed her kits off of the area chicken and guinea flocks. We found feathers all over our place along with fox prints around the coop but didn't lose any birds due to our Fort Knox metal sided coop and chain link kennel panel run with hot wire.
Neighbor lost their entire flock.
I called the local DNR. We live in rural Missouri. He told me that the only way to get rid of a fox is to shoot it. Here if a predator kills livestock and yes, chickens are considered livestock, we had the right to protect our herds and flocks by shooting the predator. This fox was proven to be a nuisance so his only suggestion was to shoot it and the kits.
He said that fox aren't called foxes for nothing. You won't catch them in a live trap but he said foot hold traps could catch them. I asked if DNR would be interested in live trapping her and relocating her to a conservation area and he said nope, no luck trapping fox in live traps and said, you all have the right to take her out. I hated to hear it. I had spotted her once and she was a beautiful animal.
I never got a clear shot at her but spread the word to the local flock owners and the problem ceased so somebody probably got her.
Sorry to hear that you are going through this. Wild life is great when it stays in the wild. But when it encroaches on farms and begins killing livestock, it is no longer something to be admired but eliminated. If you try to move it whether it be a fox or a raccoon, it just becomes somebody else's problem.
Good luck getting rid of it.