Well, she WASN'T lying. It was said in an overheard conversation in circumstances that made a lie ridiculous. Even if they spotted Hark, how could they assume he was reporting to anyone? If they were trying to feed Elayne the information, it would have been a different source. In any event, the ambush was a suprise to the beneficiaries as well - they did not know themselves that Chesmal & co were even in town, much less preparing to grab Elayne. They were not working together, and their expressed objectives were mutually incompatible. Shiane's group was given direct orders by Moridin and was working for his ends, which involved getting rid of Elayne at the appropriate time for their plan, while the ambushers were freelancing, and came to the city hoping for a chance to snatch Elayne or Nynaeve to buy their way back into the good graces of the Forsaken. There was NO way to anticipate that ambush, especially as the group was taking pains to conceal itself from anyone else.

And tactically speaking, your suggestion sucks. You are suggesting what every commentator on the internet and snarky deconstructionist ridicules characters in horror movies for doing - splitting up to let the bad guys pick them off one by one! In military parlance such a result is called "defeat in detail." That is how Rand and Mat each fought the Seanchan in Altara, despite using much smaller forces - they attacked the Seanchan when the latter split up their forces, using their greater mobility to attack and defeat each smaller force before they could combine. That is how the Seanchan general stymied Rand, leading Bashere to suggest calling it quits - he did what Elayne did, and kept his forces together, forcing the enemy (Rand; Black Ajah) to face the combined strength of the entire force.

And even setting aside tactical principles, there is the personnel issue involved. Whom should Elayne have sent in as a PMD? She did not know if Sareitha or Careanne was the Black sister among her entourage, but she knew it was one of them. If she sent in the secret Black, she would be giving the game away, by allowing her to warn the Black sisters already inside, and giving them a chance to coordinate their plans. If she sent the innocent sister in, either she would come out, reporting the coast is clear, in which case she would have missed something, or else she would get captured or killed, both giving warning to the enemy and leaving Elayne with even less resources with which to confront the Black sisters remaining. Not only that, how could she know, if the sister sent in did not return, if she had been captured or was plotting with her fellow Blacks? Or if the sister she sent DID come out reporting all clear, how could she know that the sister was innocent and right, or innocent and mistaken, or Black and luring them into an ambush? And if she sent Vandene, that would leave her alone with two sisters she could not be sure of, and either there would NOT be a trap or more enemies inside, in which case all they were doing was risking Vandene being caught or alerting their quarry, or there would and Vandene would get killed or captured, in which case, Elayne MIGHT know what happened, but only have two sisters now left to fight at her side (one of whom she knows is Black), and not be any closer to capturing them! And what would it tell her if Vandene DID get killed, and they knew because Jaem went berserk. What then? How would that have informed them of the specifics?

Either there IS a difference in the respective abilities of the two genders to grasp tactical issues, or you're an idiot. Either for not seeing a glaringly obvious scenario, or for posting about stuff you have not bothered to give a second's thought to.

Actually she said that there was nothing else they could have done. Elayne is her own harshest critic, as Nynaeve notes more than once, so if SHE says she couldn't have done any better, she really couldn't.

So sorry if she does not allow a potential Darkfriend to dissuade her from arresting the Black sisters. Regarding Min's viewing, those are ironclad guarantees. This is accepted as a fact. If Min saw that she would deliver a pair of healthy and strong babies, then she will, and that is an immutable fact. Nothing fatal can happen to her, and though she is aware of the possibility of non-fatal misfortunes, like being burned out, she is absolutely right about her safety. Until she is near term, she can rest assured with perfect confidence that she WILL survive whatever comes her way. Pretending otherwise is like making preparations just in case the sun DOESN'T come up tomorrow - maybe it won't but that would entail such a drastic re-ordering of the understanding of reality that practical planning for it would be impossible. She does not act like it makes her invincible - she simply accepts the reality of the situation, and primarily uses her assurance of survival as a way of reassuring her companions who are less capable of thinking outside the box to accept such things. She uses it to evade the excessive restrictions which a group of people with completely different priorities attempt to place on her, that will impede her ability to properly do her job. She uses it to get around Aviendha's concern that she might have endangered Elayne & the pre-kids with her activation of the library ter'angreal, and even as she reassures her dimmer sister, she is mindful of the possibility that she is susceptible to being burned out, but refrains from mentioning it to spare herself (and incidentally the readers) from another round of Aviendha's ji'e'toh-inspired self-flagellations. Without the viewing to give her the self-confidence to hold back the attempted smothering by Birgitte, Dyelin & Aviendha, she might not have been able to function well enough to claim the throne. And before you start debating that as a priority next to her kids, yes, it IS a higher priority than her children's lives, or it should be, regardless of her preferences. Her children have the same duty to Andor that she and her brother have had since birth, and for the exact same reason. From the second they are born, their lives will belong to Andor as the Daughter-heir and her future First Prince of the Sword. It will be their duty to lay down their lives for Andor if the circumstances call for it, and Elayne HAS to risk their lives and hers if the situation warrants it for the good of Andor.

THAT is what being a noble is about, or should be. The fancy clothes, the wealth, the right to give orders and act superior, these are all ancillary trappings meant to enable nobles to protect their people and serve their country. As William Wallace said to a group of nobles in Braveheart: "You think the people of this country exist to provide you with possessions. I think your possessions exist to provide them with freedom..." The same goes for being an Aes Sedai. They have an obligation to protect people from supernatural threats, because they have taken upon themselves sole authority and sole power in much matters. By forbidding channelers to even train one another outside of the White Tower, they strip the world the ability to defend itself with the Power, so any threat that requires the One Power is the obligation of Aes Sedai to answer on behalf of the White Tower. To allow a threat to people that weilds the One Power unrestricted by any Oaths or morality to walk free is, or should be anathema to sister, and to allow Shadow-sworn channelers to threaten the world flies directly in the face of the stated purpose of the Green Ajah. For Elayne to let murderers to walk free in Andor is a dereliction of her duty as a noble of Andor; for her to allow them to move freely in Caemlyn is a violation of her obligations as the military authority occupying Caemlyn; to allow One Power threats to ordinary people to exist is a failure on her part as Aes Sedai; and to allow channelers who serve the Dark One to carry out their plans is against her duty as a member of the Green Ajah. Even personally, as a mother she has an obligation to protect her children, which means removing any threat to their lives which has hostile intentions towards her own. For all she knows, "Mellar" and the sister who was murdering the Kinswomen have designs on her children after their birth. No matter how you slice, Elayne's duty, and that of her Aes Sedai companions, was to get the Black sisters. Otherwise, she would be guilty of cowardice and desertion (the proper terms for someone who places safety over duty).