Re: Marrying a non-muslim who is NOT ready to convert..
Your brother is 100% sure otherwise he would not have informed you and your family. If they are both commited to each other as it seems like they are it will work out fine.
Consider the girls family, they are going through the same doubts as your family, even more in todays climate. It was not an easy step to take for both of them.
Support your brother. I have seen personally it works out fine in todays society. Avoid listening to all those who will tell you its wrong or what is right. It really does not matter as long as the couple are happy together. If your future sister in laws family are willing to accept your brother, your family should accept her. If she is a good person that is all one can ask for. Im sure your family will be happy for them eventually.