Earlier episodes focused on that very question with those two girls and the woman who was caring for them - what is the dividing line between surviving as a human or becoming a monster? How do you deal with such horrors as an adult" How do you raise a child with such horrors? What happens when a seemingly strong person breaks?
The episode you saw was the endpoint of that thread. It was damn hard to watch, but in context it had a great deal of meaning beyond some splatterfest gore scene.
Yes it was, very hard to watch. I would also say that Carol did not "enjoy" what she had to do. She was struggling with it. There are no rules anymore in the society that The Walking Dead inhabits. You are watching what happens when civil society disintegrates. That young girl was a danger to all those around her. Carol had to do the most difficult thing, and it was hard for her to do it; but, she had to and she stepped up.
This show is asking us, "what would you do?" in these situations, when there is no longer black and white. When the rules are out the window.
I also found it interesting that Rick had to kill Sophia early on in the series (Sophia being Carol's daughter who had turned into a "walker"), and now Carol has been put into a similar situation, and she responds in a similar fashion. Neither of them would have thought themselves capable of such a thing; but, when put into an impossible situation what would we do?