Does she have any other siblings?

My suggestion is that you read up on enmeshment in a family therapy book or online.

The family is overly involved in each other and they rely on each other inordinately for support. You must understand that Prince Charming himself could come along and the family would be against him. Therefore, you must not take anything that they do to you personally. They would be uncomfortable with any and all suitors, not just you. It feels personal, but it isn't personal.

If she stays in therapy and the therapist is competent she will get guidance on breaking away from the enmeshed family and establishing a healthy distance. This will take time. In the mean time, you must not give the family ammunition by unreasonably refusing to speak to people, by losing your temper, by criticizing them. You must overlook it when they don't apologize to you. Is she worth enough to you to not fight them back? Is she worth enough to you to not insist on you being right and them being wrong?

You might want to see a therapist yourself for help in learning how to deal with them, with not taking things personally, and with not losing your temper.

Don't get me wrong: you can become a completely model citizen and they still won't like you. They are not going to like you. Again, it isn't personal, they just don't want their enmeshed family disrupted--and you are the current potential disruptor. But the sweeter and more reasonable and more patient and more forgiving and more even tempered you are, the easier it will be for her to break away from them enough to join with you. The more you get involved in arguments with her parents or sister, the harder it will be for her to join with you.

Remember: this feels personal but really it is not personal. They will find reasons to oppose any guy that comes along. Your job is to be as loving to her as you can, to entice her away, and to be as patient and even-tempered with them as you can possibly manage (work on this), so as to minimize her stress in breaking away from them sufficiently so as to join with you.

Just remember this every time before you speak or act: every time you engage acrimoniously with them, you are driving her away. Every time you are patient and civil with them, you are bringing her closer.