For the first issue of the first son (who is Hayasaka's employer) not protecting her: it's possible he just didn't know. If the third son is trying to gain the upper hand through kidnapping, then he probably wouldn't alert his opponent as to his plans....the family's third son, Unyo, moves to grab Hayasaka and torture her for the secrets she might possess. Why doesn't the main house protect its asset, if the secrets in its possession could be potentially harmful to it?
Unyo's plan is contingent on Kaguya's tacit agreement to Hayasaka's torture (as punishment for her betrayal) - but given that what Hayasaka knows is overwhelmingly about Kaguya, why would she ever agree to it?
Well, he knows it's a threat vector. He knows he's decided to replace her (and the reasons for it), and he knows she's decided to retire instead.For the first issue of the first son (who is Hayasaka's employer) not protecting her: it's possible he just didn't know. If the third son is trying to gain the upper hand through kidnapping, then he probably wouldn't alert his opponent as to his plans.
Tbf, I would expect this much - what is it that she knows? "Kaguya is a lonely kind-hearted child deep down"? Not exactly hot blackmail material, that.Another possibility is that the first son knew about the kidnapping plan, but didn't think that the information that Hayasaka had was that important, and therefore she wasn't worth the cost of protecting.
I guess that'd make sense for a Kaguya willing to see Hayasaka punished, but unable to achieve that any other way.As for the second issue of Kaguya agreeing to give up someone who has knowledge of her: Unyo stated he was counting on Kaguya to be emotionally compromised. That she'd be so distraught over the betrayal that she wouldn't be thinking clearly. Not a good plan, but he might be in a bad position in the succession war and grasping at straws.