I would let my brother know how I feel about the situation and the pain he would bring onto himself, but in the end, he's a grown man and has to live with his decisions. After I gave him my honest opinion, I would butt out and hold my tongue as best I could.
I also would welcome the child and I would be polite to the mistress, even though I probably would not like her. Being mean to the child's mother will affect the child just as badly as being mean to him/her. Kid's have such a strong connection to their parents when they're young that they feel that when people hate their parent, that people hate them as well.
I would do my best to be respectful of the ex-wife and make sure she is not placed in an awkward situation at family gatherings.
I really don't like to "rub people's noses" in their mess. What's done is done and trying to punish the brother or the mistress is just going to make things work. If the brother didn't learn what was right when he was coming up, it's too late to teach him anything at this point. Also, relationships are so complicated and are hardly ever as black and white as they appear on the surface.
The only way I would get more involved in a grown family member's business is if they are doing something illegal. For instance, if they are molesting a child, I would call the police. If they are dealing drugs, I would have to keep them out of my house until they quit, but I would look for opportunities to help them get out of the lifestyle.