You paint an ugly picture of your Mom, and if it's accurate there's not much you can do about it (assuming you've already calmly expressed your feelings to her).
Has she told your girlfriend that she doesn't like her because she is Greek, or was that your bright idea of sharing?
If she's rude to your girlfriend, don't bring the girl to your home. It's not fair to her to subject her to your mother's lousy behavior.
My mother's family was Irish/Norwegian (both grandparents were immigrants), and they really didn't like Italians. I dated several Italian girls throughout HS, and they were always giving me grief about it.
They didn't have aa problem with African-Americans or any other nationality, which made the whole thing seem weird, as well as nasty.
Eventually I learned that they grew up right next to an Italian neighborhood in NYC, and always had trouble with the Italian kids when they were growing up. Who started the trouble is anyone's guess. I also learned that my great-uncle, a Norwegian tugboat captain in NYC was killed by the Mafia for refusing to pay protection money.
Hardly logical to assume that all Italians are bad because of past incidents, but sometimes these sort of animosities have a root that isn't simply hatred of someone who is different. Maybe if you talk to your mother about it you will be able to get a better understanding of where her bigotry comes from. It won't make it right, you may no longer think of her as Hitler.