I don't know if it has already been mentioned or not; I've searched for it but found nothing. But what if William is actually proud of Alex to a certain extent? I'm replaying the game, and yes, the guy is an asshole who has made his daughter's life impossible. He even slapped her in front of us, and I'm sure it's not the first time, but thinking about it coldly, maybe inside his twisted mind, he feels some pride for Alex. She's strong, independent, resourceful, and she doesn't stop at anything or anyone to get what she wants. She even has enough talent, and I imagine mental strength, to have a shot at going to the Olympics. Those are qualities that someone like William should appreciate.
Yes, all of this clashes with his worldview where he is in control and his children must do what he says, when he says it, and how he says it, but still, he should have a certain sense of pride fot her. Alex is infinitely better than his brother, who is useless and only knows how to rely on his last name to get things, and if he inherits everything from William, it will take him a couple of months to ruin it all. And I'm sure that's not good for the Bardot name. And anyone can see that, not to mention someone like William.
In summary, yes, he's a jerk, yes, he imposes things and feels no love for his daughter, but that doesn’t mean he is so stupid as not to see how his daughter really is and to appreciate the many qualities she has, which he himself promotes.