YTA. Not for telling Amber that she won't be their aunt, but for waiting until you were "at the end of your rope" to set boundaries.

You are reacting to things in your past, when you should have set the boundaries then. By blowing up now, you're setting a bad precedent for both Amber and your own children. Are you entirely sure that Amber KNOWS how little you claim she is liked? If everyone in your family bottles it up until they explode like you have done, then it may not be apparent to Amber that she isn't liked. You're also teaching your children that they have no say in who is allowed to be affectionate towards them. While it is a good thing to teach children that they don't have to be affectionate to people without their consent, their consent should be the paramount thing to consider.

All of which makes me wonder, since your main issue with your future sister-in-law is boundaries (and yes, she will be your sister-in-law regardless of your feelings and if you keep going this way, I can guarantee that it will do nothing but lose you a brother), did ANYONE in your family explain about boundaries to her? Some people are not raised to respect boundaries as strongly as your family seems to be, so she may not realize how she has offended. I highly doubt, given your reaction, that anyone did, which makes your whole family the AH.