I can relate to your gf. Her parents only worried considering its far away. Parents are always strict when it comes to their daughter(s) specially a only daughter. If she chooses her family over you... don't complain. I actually think parents is far important than bf or gf. (Parents will always be there. They won't leave you and love you unconditionally unlike a bf or gf.) Parents only care what's good to their children. Its not controlling, they only make sure she is safe.
Also Try to understand her, if she can't come over then why not you come over to their house instead? Surprise her. Or askyour gf'sparents a permission (in person) to come over in your placeand let them know there's nothing bad will happen. Lets see ifthey will still disagree. If she's scared in one of your family members, try to comfort her and ask her again why. be sincere and let her fell you are thr to protect her. You know, girls have a natural instinct/female intuition. Most of it is right so if she's scared in one of your family members then you should be worried..
Unless she only say those as a excuses then.. you should probably think the worst case scenario. (eg. breaking up, not love you anymore etc..)
That's people for you. Trusting one another, helping one another----- it's all a fantasy. Humans are creatures that will always betray.
