Is the questioner considered sinful and (guilty of) slandering chaste, unsuspecting women because of the whispers of doubt regarding her mother's innocence, despite her certainty of her innocence and her awareness that her father is excessive in his suspicion?

The father must fear Allah and not accuse his wife without clear proof. He should have a good opinion of her unless something suspicious becomes apparent. As for the obsessive doubts about the mother, there is no blame for them. However, one must turn away from all such whispers (waswas), because persisting with them has severe consequences. Things that help in this regard include: seeking Allah's help, sincerely turning to Him, and frequent supplication.