Tofumama- sorry for your plight- this is the difficult part of responsible animal husbandry. I am posting this link because I have gone through what you are going through and wanted to share a very humane method that I used personally and works. I have since had to do this again, due to an injury another of my hens sustained that could not be fixed and it worked just as peacefully as the first time.
https://www.backyardchickens.com/forum/viewtopic.php?id=312959
https://www.backyardchickens.com/forum/viewtopic.php?id=312959
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