Unless your theory is that Alexander is Callista's father, Callista being there over any of the girls makes no sense since the mystery girl called him father repeatedly.
I am no more fixated on my theory than you are on Olivia being the secret sister, which would require a lot of moving parts
So your theory is that Olivia got secretly trained by her father, ran to her waitress job, and took care of her brother without any of the sisters or anybody else on the island knowing anything? Somehow, doing all these things, she hid her brilliance from her father? The more threads that get pulled, the less sense it makes that Olivia's the sister at the beginning.
As for hating him, Dom Juliette and Veronica hate him, Alessandra said there was good and bad. There's no need for her to lie to Kane at that point.
Uggghhh....
Olivia is Callista's daughter. Even if Alexander wasn't the father, he already knows Olivia is brilliant....because she is Callista's daughter. The whole plot kinda revolves around Callista and her brilliance and perfection...in the eyes of Alexander. Remember this, this is the actual plot...Alexanders obsession with Callista being perfect, him wanting a son. Because of this, he also knows Kane is of equal measure, being Callista's son. Why Alexander, specifically wants a son from Kane with one of his daughters. That's not opinion, that's fact, as told by the story. Olivia
is as gifted (if not more so, being Callista's daughter) as any of his other daughters.
Lots of people call an authority figure father btw...and not neccessarily in a sexual context. Egen wives depending on religion and culture. Really not that unusual around the world, however that is beside the point. I said that purely as I believe it could literally be anyone over Alessandra and yes, quite
possibly Olivia.
They also did not live on the island...why it took Veronica so long to track Olivia down....and if you think Alexander, the richest most powerful man on the planet (or one of) never left the island...well...not really sure what to say to you in all honesty. Again, even Veronica states she would not be surprised if Alexander knew where they were all along. I think given his other daughters, it's perfectly reasonable for him to think none of them could run the company (and remember, he actually
didn't want them to run the company, he wanted a son to do it, otherwise we'd have no game at all, his will would state who he wanted in charge) and that keeping Olivia a secret from the rest and letting her have a 'normal(ish)' life under the tutelage of his most precious and belovedly gifted and perfect Callista might provide different results...in the Gambit
he created...
Connect the dots. So far, in terms of story, plot, facts and hints...nothing connects Alessandra to being there at all (that's not to say she wasn't). There are hints it could be a number of other people.
Edit: Also, important to realise, who's to say Alexander didn't treat Olivia differently? People act differently towards people all the time, you probably do it yourself. Friends, family, wwork collegues you can't stand. Remember, Callista left because of his infidelity, not his attitude. His asshole attitude came after he left and i'm pretty sure Callista would never let him act like around her or Olivia. So Olivia may have only seen the Alexander that everyoine said was a good guy while unfortunately, the other sisters bore the brunt of his bad behaviour.