I'm so sorry you're going through this—it's never an easy situation.
Just to add to what others have shared: dehydration is a particularly cruel way to go, and if CO₂ isn't an option,
cervical dislocation can be a humane alternative.
This involves quickly separating the skull from the spine, resulting in immediate unconsciousness and death. It can be done manually (by firmly and swiftly pulling the head while restraining the body), or mechanically using methods like the broomstick technique or a Koechner device. When done properly, it's fast and minimizes distress.
Decapitation is another option, though understandably difficult for many emotionally. From what you describe, it sounds like she’s suffering—and sometimes the kindest choice is the hardest one to make.
If you have access to a nearby farmer, someone with a large format nail gun they may be able to assist in a quick, humane way.
You're not alone in this—many of us have had to make these hard decisions.
