This is a tough situation especially when both sides are not even open to listening when any efforts at communication are being made.
Tell your parents firmly that you wish to marry this girl (if that's what you want) and that you're not interested in marrying anybody else. Encourage your parents as the "larkay walay" to make efforts to communicate with the girl's parents. This should be done face to face. Your parents should ask the girl's parents to at least listen to them one more time before deciding upon the fate of their daughter. The parents from both sides should sit together and discuss the issue..........and I don't think it would be a bad idea for you both to be a part of this meeting/discussion. It would be good for you both to sit with both sets of parents during this discussion to ensure that you both (u and girl) see everything with your eyes and hear everything with your own ears.
^This reduces the chance of "false information" being relayed by "well-meaning" parties to either you or her.
**1) If you're that serious about her......tell your parents that you're not interested in any girl but her.
2) Have your parents calm down and request her parents for a one more meeting to settle talk things out before making any decisions. A good point to bring about with her parents is that as Muslims we should settle things peacefully and allow each other a chance for clarification.
3) A meeting should take place between both sets of parents....and you and her should be there during this meeting so you can see and hear the truth.**
Considerations:
Keep in mind that if both families don't like each other.....then this can potential create problems in your marriage. And the person to suffer most will be........the girl. If a girl has no respect in her susraal.....her life can become miserable. And this is chance that you will have to be prepared for if you succeed in marrying this girl. If your parents continue to hold a grudge toward her......keep in mind that you will have to support her if they give her a hard time after marriage.
^Is that a risk and challenge you are willing to take? If so.....give the issue your best fighting shot.
I agree. If ur 100% sure of the girl be firm (if u waver ur parents will say 'oh, u aren't serious, u must not like her that much anyway') but also remember compromise is the key. My Mum was very against me marrying a non-desi at the beginning but now she loves the idea and thinks he's great so parents can do u-turns if u talk to them and try and convince them in the right way. Good Luck :)