Now we are having a good conversation.

Thank you for the opportunity. That is what I was hoping for. So I am going to give answers for all your current questions. And if you have more… just bring them on. No evasion here!
How about: what it is about suffering that’s NOT terminal that makes you say–you can’t kill this person?
I would not. As long as there is a reasonable hope for recovery, AND as long as it is her wish to keep on her fight, I would support her in every way possible. But, then again, I would support her decision to commit suicide or demand to be euthanized, if that would be her desire. Let me be clear. I respect the decisions of lucid, rational adults to make reasoned decisions
for themselves, even if I do NOT happen to agree with that decisions - as long as those decisions do not affect others. That is what I consider a loving and caring approach.
But, of course, nothing is ever simple. Our decisions might affect others. If the sufferer’s decision to be euthanized adversely affects others (loving relatives) that is the sole problem of the decision making sufferers.
And what about the one about whether it’s permissible for a mom to make a decision for a child who’s terminally ill and suffering?
SMALL children cannot make reasoned decisions for themselves, and we acknowledge this fact when we allow the parents to make the decisions for them - even I extreme cases.
And what if the father disagrees?
They have to come to a conclusion among themselves.
Also, what about the one where you said you’re not an absolutist but then said “I advocate the right of everyone to make decisions regarding their own life”–Isn’t that an absolute statement? And if not, what are the exceptions?
Be careful about the usage of “absolute”.

It was a very short post, without going into details. Obviously I was referring to lucid, rational adults, who are recognized to be able to make decisions for themselves. Not an “absolute” declaration, which would be: “anyone and everyone, even the mentally impaired, or the ones under the age of reason should be allowed to make decisions about themselves”.
That is why one must be careful about using the “universal operator - ∀” (as opposed to the “existential operator - Ǝ”). it can lead to all sorts of logical problems.
I would take her out of her misery: I would give her painkillers.
There is enough pharmacological knowledge that we have the ability to, if not totally eliminate the pain, mute it.
Since your profile shows that you are a nurse, you must be aware that people can develop a tolerance against pain medication, so that the medication will become ineffective. The only medication that will be effective will also terminate the life of the sufferer. So when you administer the necessary amount of morphine (for example) you are also aware of the fact that it WILL result in death… even if your intent was only to suppress the pain. You know… the paradigm of the “foreseen, but unintended consequences”.
I would never kill someone in that condition.
Which is just another way to say: “I would let them be in horrible pain, without the hope of recovery”. I have no problem with this approach, even though I disagree with it. To allow someone to suffer against her wishes is cruel and wicked - in my opinion, of course.
Why? Because human life is so precious that there is nothing that could induce me to take it from an innocent person.
And here we reach the final point. Life is neither desirable nor “precious” per se. Good, pleasurable, loving, pleasant life is “precious”, while painful, suffering life is not. In my opinion, of course.