Per the screenplay, it was the boy's mother, named as Jennet Humfrye
EXT. EEL MARSH GRAVEYARD. NIGHT.
Arthur and Daily stand in the mist before Jennet Humfrye's
headstone, Arthur cradling the shrouded body of her son.
At the foot of the headstone there is now an OPEN GRAVE.
Beside it, a pile of DIRT and a discarded SPADE.
As we follow Arthur's gaze into the hole, we see that
Jennet's CASKET is visible.
Arthur hands the child to Daily and jumps down into the
darkness of the grave.
EXT. OPEN GRAVE. NIGHT.
Straddling the casket, Arthur pries open its lid.
Inside we see JENNET'S REMAINS - just bones now, and shreds
of her tattered black mourning gown and veil.
Daily hands the boy down to Arthur, who places the child
gently into the coffin beside his mother.
One last look, then he replaces the coffin lid.