Full disclosure, I never cared for the character of Cadsuane. My favorite scene is when Tam al'Thor refuses to accede and calls her a bully to her face.
It occurs to me that this may be the intent behind the character, that she's written to be a certain degree of unlikable. Robert Jordan clearly intended her to be a force of nature, bending others around her to her will. She extensively used force to kidnap and manhandle people, Aes Sedai, even sovereigns to further her plots.
There are several passages where the White Tower hierarchy is shown to be based upon strength in the power and several characters are critical of this power structure. Several Aes Sedai are shown to admire, even long for, the power structure of the Aiel Wise Ones, where strength in the power has no bearing and instead the strength of character or strength of will is the measure of a woman. In this light, the writing of Cadsuane's abrasive demeanor can come off as an indictment of this power structure.
However Cadsuane confides in Sorelia that her goal is for the Dragon Reborn to reach the last battle alive, and she believes it is critical Rand relearn to laugh and cry. In pursuit of this goal, Cadsuane doesn't seem to alter her tactics a whit. She's all business to the point of barely even expressing a sense of humor, not even a serious or deadpan one; but she intends to teach laughter. She's certainly capably of bullying someone to tears, but that doesn't seem to meet the spirit of her goal.
In the end, Rand almost kills his father due to the passing mention of Cadsuane's name. But he pulls back and sets out on the journey of self discovery that ends on Dragonmount with the reunification of Rand and Lews Therin. You could say Cadsuane brought about her goal by causing such fury in Rand that he had to choose madness or sanity. I don't accept that was Cadsuane's intention, just happenstance. Even if attempted patricide were her plan all along, it seems a reckless, dangerous gamble to hang the fate of the world in that one moment.
Setting aside my opinions and speculations – I invite your differing perception, especially if it frames your answer – to the questions:
- How did Cadsuane determine laughter and crying were essential skills for the Dragon Reborn?
Admittedly it's pretty clear from the narrative that Rand is heading down a dark path, and even hinted that he would have made the wrong decision in how to properly defeat the Dark One during the Last Battle without his epiphany. But how did Cadsuane know that? She seemed to have her goal set in stone before (or perhaps shortly after) meeting Rand for the first time.
- Did Cadsuane ever reflect on the unsuitability of her tactics to achieve that goal?
Rand doesn't seem to trust her right from the start and her strong-arm tactics often have the opposite effect, making Rand harder and more unfeeling. Cadsuane never seems to change track with Rand and it finally takes a different force majuere
- Did Robert Jordan or Brandon Sanderson comment on why Cadsuane's personality was ill suited for bringing Rand back from the brink?
Obviously this incongruence achieved a lot of dramatic tension, and the Rand + Tam meeting made for a great story, but I was expecting Tam to play a direct part in Rand's metamorphosis; to achieve Cadsuane's goals. Maybe it's an anachronism to expect a consoling, caring personality to take the lead in treating someone's trauma. Maybe I just prefer it when the "Good Guys" get along.