I'm upset at my girlfriend getting angry with my family
Family first, always.
I like her and I don't want to separate with someone I care about
It is good to have a healthy relationship with conflicting opinions. You should both be respectful and not harm both relationships.
No, I don't ever want to be respectful.
As much as I respect your opinion, you've got to find the right balance between the two. Family is just as important as your relationship with your girlfriend, and the best thing is to sit down with both sides and have a thorough discussion, getting whatever it is off your chest. That way, you can begin to build on both relationships.