Is she really non-violent? She seems to have a pretty big violent streak in her actually. She walked around town thumping people with a stick when we first met her

This is one of my pet peeves about Nynaeve criticism, hearing from both readers and characters. Yes, there is a HUGE difference between doing harm to people, and physical chastisement! In fact, you could say that the relationship between the two is inverse, since physical chastisement can make an impression and curtail bad behavior that will lead to socially-applied corporal punishment, like flogging or execution. "Spare the rod and spoil the child."

I don't know if this was RJ being ironic or stupid, but the scene when Elayne and Aviendha are amused at Nynaeve's interactions with the Sea Folk gets on my nerves, because they are too ignorant to realize Nynaeve is right and they are the blind idiots.

Nynaeve told the sailor to let them up or she'd smack him or some hyperbolic expression of intended chastisement. Elayne's "peaceful" alternative was to have the sailor tell his bosses that they knew the Sea Folk's greatest cultural secret. Nynaeve points out that the Sea Folk are likely to be concerned about Elayne's potential to be a security leak, and to the younger women's' great amusement, rebukes her saying "Only a ninny thinks she can threaten people". And everyone thinks Nynaeve is being dense or hypocritical. But Nynaeve threatened someone with minor & inconsequential acts, and really only as a point of emphasis. Saying Nynaeve is violent for her comments about boxing ears is like accusing everyone who says "Fuck you" of intent to rape. But Elayne, on the other hand, profoundly threatened the greatest secret of the Sea Folk, one they hold very dear and are desperate to protect. They are terrified of the consequences of the Tower's ire, and the practical consequences would be immense, not only with the loss of a significant set of assets in their struggle against the elements, but members of their actual families. From the Sea Folk point of view, learning that an Aes Sedai knows about the Windfinders, is like anyone else learning that the Seanchan know about his sister who's a wilder.

And Nynaeve was right. All the unpleasant aspects of the bargain they ended up making were demands made by the Sea Folk to allow the Windfinders to protect themselves from Aes Sedai, by ensuring that they had the knowledge available to meet Aes Sedai head on, and that Aes Sedai could not use the relationship to conscript the Windfinders or force them to remain in the Tower. This is pretty much the reaction to Elayne's ill-considered comments. Not that the blame is all on Elayne, short of using the Kin as intermediaries, which was not an option available at that moment, there really would be no way to enlist the Windfinders' aid without revealing their knowledge of the secret. To recapitulate: Elayne and Aviendha smirked at Nynaeve's admonitions against threats, because the latter made hyperbolic personal threats of physical remonstrance, while Elayne merely threatened an entire society with dissolution and economic disaster!

Nynaeve's entire character is all about Healing and helping and protecting, and she has a well-established distaste for actual violence. Sure, she might make idle comments about preferring a sword to the One Power in her earliest days of training, but once she had been out and on her own, and encountered warfare, she adhered faithfully to the Three Oaths, especially the parts about not using the Power as a weapon, and stuck to it in the face of Egwene's complaints. She worked herself into a fury to Heal Aviendha's cousin by meditating on the violent actions that led to the wounds in the first place, and the idiocy of her companions exacerbating the injury by moving her in deference to the same sort of mindset. In Stone, she expresses her contempt of warfare, regardless of the motivations or justifications. She's practical, she accepts the necessity for armies and soldiers and security and the like, but she absolutely hates the end product of violence, which is injury and death, lives being cut short of their potential. She doesn't have any of the bullshit we tend to associate with non-violent movements, and she isn't the type to go around imposing her perspective on others (no, she actually isn't, Nynaeve is a badass in a pussy world, and people are intimidated by her when they have no reason, but she has no problem with people standing up for themselves [and don't bring up the Kin, either; Nynaeve wanted them to stand up for themselves by not letting others impose on them and treat them like second class people; unfortunately, Nynaeve keeps forgetting how most people are assholes, and if they are not kept on their knees, will go for your throat - she was not upset about the Kin standing up for themselves, she was upset at them turning around and trying to impose their nonsense on her and her companions] ), so we tend not to think of her as non-violent. Nynaeve is violent in the same sense that surgery is violent - the issue is intent, the narrow focus, and the necessary will, knowledge and discipline in application. Nynaeve has all of that in spades.