Honestly, I would outright ask her what she doesn't like about him, and why this thing she doesn't like so strong that she wants you to break up with him. If you find that she can't really give you a legitimate reason why she doesn't like him (such as something related to his personality, behavior, etc.), then it really might be because she is racist. I dunno how direct you'd want to be in confronting her about it, but if she can't give you real answer, personally, I would ask her flat out if she doesn't like him because he's Vietnamese?
I have a friend who's in a similar situation, just in reverse. Her Vietnamese boyfriend's mother doesn't her because she's white. She's having a hard time dealing with his mother because she is so closeminded, but hopefully your mom isn't as bad as his
