There's nothing that you can do about the argument now except learn from it.
Here's a couple of things:
She started saying that American parents will never love a Vietnamese girl and I just went against everything I knew I should say. As much as I knew I should stay calm and stay positive I couldn't stop thinking that she was verbally attacking my family.
Did you remember that the attacks aren't actually about the target? That might have helped greatly to remain calm.
She had no reason to think that my mom didn't like her because she was Vietnamese.
That isn't a fair statement for you to make and is very invalidating. She may very well have a reason to think that. Even if it isn't a reason that you can see or believe. That doesn't change that she felt that way
at that moment.
I really do realize that she has a disorder and she paints people black or white based on how they feel but my mom has always been super nice to her and I felt so disrespected that she would say that about my family.
I'm sure that you did! I would feel that way too.
I told her that she was being rude, disrespectful and selfish. I said that my family invites her to everything and has shown her only love and all these things she is saying is just fears she puts in her own head on not reality. I knew it was wrong to say this but I could not simply validate her attacking my family like that. I had to say something. Of course she said I didn't understand her feelings and got silent for an hour.
She's right! I agree, you didn't have to validate what she was saying about your family, but invalidating her probably wasn't the best choice. I'm glad that she calmed down quickly though.
I'm sorry if this is upsetting to you. It isn't meant as a criticism. It is meant with respect and to try to help you see and reach your desired goal. Each of us that tries to save and improve our relationships have to learn different ways of communicating.