YTA. I can't tell if you are being intentionally obtuse in an attempt to deflect or if you're really dense enough to not know that your girlfriend is upset that you made no effort to defend her, her family, her culture, or her home. Your mom made a completely innapporiate and downright insulting comment to your girlfriend and her family. The only thing worse then her behavior was the fact that you sat there in silence while this was happening.

This will effect your relationship as it has completely changed the way your girlfriend and her family view you and your family. She probably won't trust you to stand up for her in most circumstances, especially against your mom. In all reality, I think your relationship won't recover from this, especially as you are attempting to defend your actions with "well, I warned you".