No, you aren't in the wrong. The person who is in the wrong, is your girlfriend. She should have stood up and defended you when her family attacked. It's obvious her family doesn't care for you. Your girlfriend is in a tough spot, but she's an adult. Unfortunately, unless she stands up for what she wants, these problems will persist and make everyone miserable.
If she doesn't grow up, then you need to rethink your relationship.
Also- good for you for standing up and NOT PAYING her family!