You're right, they were going to die no matter what, clearly her only option was to kill them in some brutal manner, drag their bodies outside, set them on fire and then tell no one about it.
So I guess letting them die in the throes of a disease, choking on their own blood is the kind thing to do. Again, why were the sick residents told to shut themselves in their cells? It was an acknowledgement that the "flu"--untreated--would kill, and you know the rest. Karen was breaking down, coughing and there was no treatment in place to help her.
There's a difference between killing someone out of mercy because they are suffering from a disease/about to die anyway and killing someone to try and prevent the disease from spreading and let's not fool ourselves, Carol was doing the latter.
In that situation, maybe, killing them was the more "humane" option. Maybe. But it'd also depends on how they were killed. which we don't know. We'll assume Carol killed them by stabbing them in the head or something which may be sufficient enough to kill someone instantly and painlessly. (I doubt it, but as suggested in the show it's enough.) But, again, Carol's motives weren't this pure. She was foolishly trying to prevent the spread of the disease by killing these two people, in isolation, after the disease had already likely been spreading around the prison for a few days.
Since they were in isolation they were no threat to spreading the disease, Carol increases that risk by exposing herself to them (covering your mouth with a do-rag isn't enough to prevent yourself from catching disease. Wearing a mask protects other people from *you* not the other way around.)
If it was a true mercy kill because they were truly sick beyond recover why all of the cloak and dagger?
Because a certain "leader" was not up to accepting the reality of the disease, and would make assumptions based on emotion, rather than a practical need.[/QUOTE]
Rick wasn't the leader at that point, "the council" was, which Carol was a member of. If she thought killing people was necessary in the final stages of the disease for mercy, or to prevent the spread when the sick were at a point of inevitability then she could have argued for the "mercy kill" at a meeting; or done it and explained her actions at an emergency session.
Unilaterally making decisions for everyone and acting on them without input from everyone else is what Rick realized was the wrong thing to do which is why he handed the keys over to the council.
Carol did what Rick would have done, made a sweeping decision for everyone without inside input.
Was it the right call? Maybe. It can be argued making these sweeping decisions is the better route instead of talking about them and discussing them at length considering the type of world they're now in. Rick was, arguably, wrong in stepping aside. But at that point it seemed they'd settled and were mostly safe so there was little call for a Ricktatorship and even now Rick more-or-less accepts other input when making decisions instead of his way or the highway.
But, Carol still made a decision to kill two innocent people who were of no threat to anyone. They were isolated in their cells away from the prison's general population, presumably containing the people who were sick with the "flu." But, logically, they had to know more people were sick because exposure to viruses isn't so easy. Killing Karen and David was pointless. Anyone who was sick or was going to get sick already were and the two people displaying the most severe symptoms were isolated. Mercy kill? Sure. But that's not why Carol did it and even she says as much. (In "The Grove" she says she did it to prevent the spread of the disease.)
Motivation matters more than outcome, in most places I could be dying of a severe illness, my death being imminent and foregone conclusion with no hope of recovery. If I ask you to kill me and you do it you're still going down for manslaughter or murder no matter to motivations or my requests.