What epiphany does the grandmother have at the end of Flannery O'Connor's story "A Good Man Is Hard to Find"?

At the end of Flannery O’Connor’s short story “A Good Man
Is Hard to Find,” the grandmother has an epiphany – a sudden realization – of sorts. I
say “of sorts,” because it isn’t clear that the grandmother is entirely or fully
conscious of this realization, and it is clear that the revelation
lasts for only a split second before she is immediately shot and killed by the
Misfit.

O’Connor, referring in the first sentence here to
the Misfit, describes the crucial moment as follows:

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His voice seemed about to crack and the
grandmother's head cleared for an instant. She saw the man's face twisted close to her
own as if he were going to cry and she murmured, "Why you're one of my babies. You're
one of my own children!" She reached out and touched him on the shoulder. The Misfit
sprang back as if a snake had bitten him and shot her three times through the
chest.

The grandmother has
increasingly been in a state of paralyzed shock as she realizes that the Misfit and his
henchmen are systematically murdering her entire family and that she, too, is about to
die. She has been saying anything she can think to try to save her life. However, as the
Misfit reveals his own spiritual torment and his own deep emotional pain, the
grandmother responds in an entirely unexpected way: she reaches out and tries to comfort
the last person on earth to whom she might have been expected to show compassion. Her
“epiphany” – her realization that the Misfit is “one of [her] own children,” lasts only
an “instant,” but it is enough (O’Connor implies) to transform the grandmother’s
spiritual existence and perhaps to begin the transformation of the Misfit as
well.

It’s important to emphasize that O’Connor does
not present the grandmother’s perception and conduct here as the
products of deliberate, rational choice.  Doing so would have implied an entirely
different kind of “epiphany.”  Rather, O’Connor presents the grandmother as an
instrument of God’s grace. God is using his own power to transform the grandmother and
also to literally reach out, through her, to the Misfit, so that the Misfit, too, is
granted a sort of epiphany. The grandmother is not responsible for the epiphany she
experiences; God is. The grandmother’s life is transformed, in its last split seconds,
not by the grandmother but by God. O’Connor argued (rightly) about this particular story
that the grandmother is both the beneficiary and the instrument of God’s grace. Her
epiphany is God’s gift, both to her and (if he will accept it) to the Misfit as well. 
One may agree or disagree with O’Connor’s theology, but her explanation of what happens
in this tale seems far more convincing than any other.

Some
readers are shocked by the grandmother’s behavior: why, they ask, should she reach out
to such a vicious person? Isn’t she just being manipulative one last time? Why doesn’t
she resist him? Isn’t her death meaningless?

O’Connor would
have said (rightly) that thanks to God, the grandmother is the one who wins this contest
with the Misfit.  Each of us, after all, must die, but it is the grandmother who manages
to live, if only for a moment, in the truest and deepest senses of the
word.

Little wonder, then, that our last vision of the
grandmother shows her, with her legs “crossed” under her like “a child’s” and “her face
smiling up at the cloudless sky.”