Let me make sure I got this right. Do you think that Callista's seven-year-old son apparently got pissed at his mother and ran away from home, and his mother didn't notice shit, but Yvette is supposed to notice her daughter being isolated from kids in a park the moment that it happens?
If Callista's house is right by the park, you don't think she let the kids just go and play there on a regular basis? Secondly, where are Callista and Yvette having this alleged meeting? If Kane and Callista came together, then they CAN'T be meeting at the play area, else Kane would have seen what happened to Veronica. Therefore Yvette, Callista, and Kane have to be away from Veronica long enough for her to approach the play area, try to play, get rejected, and then run off, all out of site of Kane. Did Yvette really leave Veronica in a place that she has never been to or doesn't remember being previously (assuming it's the same park, but Olivia does say the family moved around a lot)?
Elena getting her kid stolen from her is negligence? The hell?
Good grief, NO, read the game. Callista said Elena was neglecting Olivia, and that she was the one actually raising the girl before the Leaving, and Elena agreed. So if Callista's actions are "overprotective", according to you, then what, in your mind, made Elena's treatment of baby Olivia even worse than Callista's lifelong treatment of Kane?
As for the rest of the stuff, this update explains Callista's reason for the gambit.
... WHERE?
C: If I refused [to raise Olivia] or let [Elena] know somehow...Kane's life would be forfeit.
...Then Alexander died.
... I knew it was safe to send [Olivia] back to [Elena]
So, Alexander kills Kane if either a) Callista doesn't raise Olivia, or b) tells Elena. When Alexander dies, Callista knows Kane is safe if she breaks "b". Why then is she letting him be put on mortal danger in the Gambit? She never said Alexander would kill him if he didn't do the Gambit, and she literally said that he is no longer a threat to Kane due to his death.
Bring peace to the companies? Again she said that the bridge is Olivia AND Kane, and rounding down to 4 Gambit fates for Kane (Head, middle-management, slave, dead) therefore only a 1/4 chance of success, and equal chance of death. Why is this route necessary? Wouldn't the safest route be to bring Kane with her to his family, while Olivia takes over KG, with the classic "divide and conquer"? How would making Kane head of KG ensure peace with DS anyway? They could just see this as a betrayal.
It's not the end of the world, that was just discovered, and again, best path for Kane would be DS with Olivia as KG head.
All this doesn't change the question: why is it necessary to ensure Kane does the Gambit? Where is the threat of his death, which is Callista's tip priority, coming from? Who's going to kill him if he never enters the Gambit? This is the single biggest unanswered question of the whole game.