I agree. They don't have a dog in the fight and don't need to be put in the middle.
I sort of agree with this. If you don't know the other people at all, then you shouldn't have emailed them. Your mom also needs to learn about BCCing people instead of letting everyone's email address be visible.
Having said that, one time I tried to handle a similar situation in the same way, by only emailing the sender with a correction about a racist story that was untrue. All the people copied on that email know each other. And, after I'd sent the correction, someone else replied all basically saying how awful the people in the (untrue) story were and she'd emailed everyone she knew to pass it on to them. So I replied to that person too, telling her the facts. Then someone else emailed everyone agreeing how racist the horrible people in the email were. 
At that point, I replied to all and included links to two different sites debunking the story and showing how it was totally untrue. A few people replied to all and thanked me for correcting the issue. At least, at that point, no one was sending it on, but I wonder if anyone bothered to contact those they'd emailed to say the racist story was untrue.
Exactly. I also don't really see it as being put in the middle. They either agree with the content of the email, or they don't. As a person who didn't agree, I'd feel glad that somebody was challenging this garbage. If I did agree, well, those views deserve to be challenged!
Especially if, as in this case, it is easily proven that the incident as related did not happen at all, so anybody looking to have their hateful views bolstered by this filth would have the rug pulled from under them, and would not send this email on.
If I was at a dinner party, and somebody started mouthing off in a similarly offensive fashion, I would pull them up on it. I didn't create the embarrassing situation, they did, when they started sharing their bigotry with the group. I'm just putting an end to it.