Sanjay, the very fact that your girlfriend is refusing to marry you, for whatever reasons, makes it amply clear that she is a girl who has got her priorities set. I don't think that her fear that her father would beat up her mother if she marries someone without their consent is an emotional decision. It shows that she is someone who can face issues with maturity and knows what is right and wrong and is capable of taking decisions keeping the future in mind. Do you think it would be nice if she joins you in life by destroying the relationship between her parents? I personally feel that her decision is wise.
In this context, what I suggest is that instead of trying to convince her, why don't you make an effort to take the matter to an higher level? Why don't you involve your parents/elders and let them discuss the matter with her parents if she is willing for that. Instead of treading on the same path without being able to reach your destination, it would be better to take deviations and see if it could help. If after all the efforts, it appears to have reached a dead end, put your relationship under the carpet and start life afresh.
Everything will subside after sometime and you will find yourself happy that you have not given into emotional pressures and is in a position to plan your life with clarity. Be practical! All the best!
'Our knowledge is a receding mirage in an expanding desert of ignorance'- Will Durant.