She knocked, and was perhaps admitted by Thalassa, and went up to her father's room.

What happened during that interview?
We do not know, but we are told that Robert Turold was a man of harsh, unyielding disposition, the slave of his single idea, which was the acquisition of a lost title.

Such a man was not likely to be moved by pleading or threats.

We must imagine a long and angry scene, culminating in the daughter snatching up her father's revolver and shooting him." "Thalassa told Pengowan that Robert Turold kept the revolver in the drawer of his writing table," Dawfield remarked.
"I have read Pengowan's report," returned Barrant impatiently, "and I am assuming that Robert Turold's daughter knew where it was kept.

This is a purely constructive theory of her guilt, and we have to assume many things.