Man, do I know where you're coming from. My boyfriend's mom hates me too. I know it hurts and you want approval, but if your girlfriend truly loves you, she'll stay with you. I'm also in a long distance relationship, 1 year now and my advice is just be patient and polite to your gf's mother. I know it's hard. Tell your girlfriend that you will not let anything come between you and her. That shows a lot. Good luck.
Typical mother reaction, don't worry about it. If you 2 actually love each other that much of course. My overseas friend's parents don't really like me either despite the fact they don't even know me & it's understandable since I'm a guy half the world away & they're simply protecting their daughters.