I will start off by saying that I am approaching this topic as a complete novice. Having said that, there is a lot of weight carried with the phrase "the customer is always right", and in this respect I fully understand why other posters would pick up on this and in turn be critical of how you handled your client.
However, I do think that people are missing your comment in your first thread whereby you say that your client was slating a lot of other nail techs, and how she said that every time she had had her nails done they always come off within a few days. Because of this comment, I would say that that is enough to assume that the fault lies with her as opposed to being critical of you and your own abilities as a nail tech. Those that were critical of you in this respect I do feel are being unfair because of this.
As for your reply to her (where you finish of by saying that she can remove you as a friend on Facebook etc), I do think you are completely justified in thinking/feeling this way, but not justified in actually saying it to your client. The best customer service approach is to always bite your lip, not say anything other than that which the client wants to actually hear. The products you use may not be cheap, but then negative word of mouth can and often will result in it being more expensive for you in the long run. What would you rather prefer - a client who is unhappy and bad mouths you, or a client who is merely satisfied and thus doesn't say anything bad about you to others? Which is the more damaging scenario to your own career? My point being, if she ends up satisfied, then she may well come back and/or she may well not say anything negative to other potential clients, meaning that they in turn may still come to you.
It's a tricky one, granted. But then customer service is a tricky area, so such situations are ones which should be expected at various points in your career. I do understand your point about not wanting to deal with her again, but customers are more influential than we often think. Hence - bite your lip, take the criticism (even if you are certain it's unjustified), and that way it will limit the damage such customers can (and are able to) cause to your reputation.
Anyway, that's my advice. I am a complete novice when it comes to this industry (like I say, I am yet to commence my own training), but I do deal with such situations in my other work, and alas I've found myself in situations in which I've just had to take negativity/unjust criticism on the chin and, well, suck up to clients. As someone else said in this thread, they are your only source of income.
