That isn't a threat, that is announcing her terms. You can think they are in their own right to taker her up on it, but its not a threat.

Also, as far as I know for a "einseitige Freistellung" (one sided decision to no longer want her to work there) Google would have to show that she destroyed the relationship of trust with Google, by e.g. criminal acts or maybe using her position as a manager to undermine the companies overall direction, e.g. by her going to the public mailing list afterwards.

Announcing that she wants to leave if this can't be resolved would NOT qualify as this.