The father KNEW Keira was his daughter and that the 2nd wife did not cheat on him. The reason I believe he chose to entertain that lie was that there was a prophecy that stated that there will only be "one Parvis daughter with spirits powers" and another who will deceive causing a calamity.
However, in addition to the fact "Cosette" is supposedly the daughter of the wife he actually cared for (although refused and failed to protect from 2nd wife family). Whereas, Keira looks like the wife he had no feelings for but was forced to marry due to her overbearing family's political might. Whom he hates.
I think subconsciously he thought this was like killing two birds with one stone.
He gets to be with the daughter of the wife he actually cared for and she gets to be the "Parvis Princess". And by getting riding of the "bothersome" daughter he gets the praise of "stopping the disaster".
The oracle in my opinion was just a pretext he demonstrated by his pattern of behavior countless time what this really came down to was -favoritism.
He *preferred Cosette to be his daughter than Keira.
The scene where he believes the lying maids over why Keira punished that maid who insulted her to her face shows a glimpse of what he really thought of Keira - someone he innately disliked.
She desperately wanted his approval and attention as a child and even through herself down some stairs to get it - in vain. Whereas, Cosette is able to gain the sympathy of the Duke and even "father/daughter" time and perks reserved only for family members within a short period of time.
I still don't get why Keira had to die. Most extreme scenario imo, would've just been her expulsion of her title (which is also a role of bs) either way... the 1st timeline father made no sense, I hate him.