In "A Good Man Is Hard To Find," why does the grandmother murmur"you are one of my own children" to the Misfit?"A Good Man Is Hard To Find" by...

In the context of O'Connor's story, "A Good Man is Hard to Find," grace is something often undeserved, a force outside a character that generates an epiphany.  The grandmother has such an epiphany and receives grace as suddenly looks at the Misfit with a new perspective, seeing him as like unto herself.  At this point, the grandmother becomes a good Christian as she reaches out to the Misfit.  After he shoots her, the Misfit does recognize her transformation, for he says,

'She would have been a good woman...if it had been somebody there to shoot her every minute of her life.'

Significantly, after being shot the religious number of three times,  she falls over her legs which are crossed under her, symbolically like the crucified Christ, who died to save others.  For, after turning down the road to error, the grandmother redeems herself from the petty, materialistic life which she has been living.