Her parents hates me and threatens me, ect our relationship is miserable but we want to stay together..advice?

We're both girls' so we knew that her parents wouldn't condone this, and her mom REALLY doesn't like it all. In fact, she hates it. My parents don't care and I put up with her mom. She threatens me and all that good stuff. She chases my girlfriend down wherever we go and makes a scene out in public, then yells at me calling me names and such. I really like my girlfriend. She said breaking up would be the best thing for both of us since her mom makes this whole thing a workout, but I told her we both didn't want to. So no. We can't hang at my house, because her mom comes and bangs on my door demanding her to come home and my mom and sister have to deal with that and she doesn't want to drag my family in. We hang outside. Constantly, she hates the cold. We always try to find a spot to hang but we either get too cold, or the cops kicks us out, or her mom is creeping. It's the same thing over and over. And when she comes home, her mom bombards her with questions. We do not want to break up. I don't want comments like heads up ect. We need help. How do we tell this woman to stop and accept us? When she was raised in a way where all of this is absolutely taboo. We don't want to hide...And I don't want her to go home to this crap. Please, it's been like this for over three months, but we had a thing since january, so well over four months going into five. Please I tried telling her that we'll just muddle through it and make a stand and don't budge, we are already, but she just makes our relationship miserable even though we do have fun together she just wrecks it. It affects where we can hang out, where we walk and when she sneaks out and says she's going for a walk, they call her and track her down on that AT&T program thing. They blocked my number. And when they pick her up, I have to leave before they see me with her. mdaosjdafknabfahdad they are so full of mad.