The Big Three ("B3" =Veronica/Elena/Yvette) state that Alexander's ultimate goal was a son from him and the perfect woman, or at the very least a son period, and the other sisters confirm this second goal. So why would Alexander destroy either of his lifelong goals is if Luke was his son, by Callista or otherwise. Veronica confirms in a B3 meeting that Kane is THE son of Callista (so Seth isn't her blood son). If the accident "was no accident" and Callista was the sole survivor with as powerful, careful, and paranoid of a planner as Alexander, he arranged it to ensure that Callista survived, and that she was the only one that could. He banged both Elena and Yvette, who had given birth before Callista even fled (pregnant with Kane upon flight, and age gap between Olivia and Kane).Ok, it's time to cook. Here’s what I think based on everything we know so far. I'm not spoiling because this is mostly speculation. Luke is likely the son of Alexander and Callista; once that accident happened, which killed Luke, Alexander probably blamed Callista and started slinging dick everywhere.
This leads us to ask why he got rid of Olivia. Was it to punish Elena? Doubtful, that was just an added bonus. I imagine he didn’t want Olivia around him because she resembled one of his sisters, and he didn’t want to be around a constant reminder of what he lost. So in exchange for getting rid of that reminder, he “let Callista go.” Even though I doubt he wanted her around anyway after Cole knocked her up.
As for the daughters. I believe that Astrid is probably older than Alessandra. It likely explains why Alessandra seemingly got off so easily. When we first play the game, we learn that Juliette and Dominique are favored to take over the company, and Veronica is a genius. We later learned that Alexander wanted Astrid to work in the family business, but she didn’t want to play ball. Yet, he largely ignored Alessandra. Why’s that? Because he likely ignored her, and she played up the whole party girl daughter to encourage him to think like that while plotting from the shadows.
One final thing about Grym Gudinna, which is likely unimportant to the overall picture, but it’s a decent revelation. Grym Gudinna translates to cruel goddess in English. Even if you believe the walkthrough didn’t give spoilers away, you can immediately eliminate two of the sisters, as neither Dominique nor Veronica would refer to themselves as that.
I'm not sure where you're getting that Alexander ignored Alessandra, as she also went through the trials, but she apparently sees her older sisters as being too soft, as they complain about having "invisible scars" while Alessandra views it as "Oh just boring past events that were of no issue" (in so many words). We also learn right off the bat that she's a mathematical genius, and thus runs all of KG's accounting, which apparently isn't a managerial position, which she states she prefers that lack of drudgery-- I mean: responsibility.
I'm also not sure how you can conclude that Dominique and Veronica, who have self-described as being "cruel" and even performing/perpetuating evil, would therefore not refer to herself as "cruel goddess". Furthermore, Callista is supporting Grymm, but Elena will confess that an evil Olivia will effectively make "Callista roll over in her grave after seeing you take this path," so who would a good "good Callista" support in the Gambit?