It's not about caring for their approval. You don't have to like them, or care what they think.
This isn't about you. It's about your missus. You do whatever she wants you to do on this, IMO. If you care about her, you want her to be happy. Compromise is the key to every successful relationship - if you don't want to do this, then maybe you shouldn't be together.
Sounds like your brother-in-law is a git, let him prove this by politely and calmly asking him to explain his issues with you in front of witnesses, after which point either the air will be cleared or you have the ultimate moral victory and never have to speak to him again.
As for her sisters, well, you may not care for them but she obviously does. They are her family, they've known her a lot longer than you. We may not get the chance to choose them, and we not get on with them that well, but we can usually have a reasonable expectation that our families will continue to be part of our life forever, whereas the spouse role is one we can only hope is permanent. You need to help your missus to keep peace with her sisters, even if that does mean going to spend time at their houses when you don't want to. Sounds like you haven't exactly made much of an effort to impress your suitor-bility on them by actually making an effort to show how well you get on as a couple.
Putting anyone in a position where they have to choose between you and their family will always backfire in my experience. Up to you though, obviously.
Maybe I am misunderstanding you, or maybe I am not making myself clear. I'm not looking for an elegant way to cut the girlfriends family out of her/our life. And I completely understand that her family is important to her. I live with her. I speak to her every day and I have seen how upset it has made her, that because of her brother-in-law, she is essentially no longer welcome to step foot into their house. I haven't thrown my weight around, forcing her to make a decision. She is taking the lead on how to deal with this. And she has done, ever since she first told me that *someone* in her family didn't approve of our relationship. Which was well over two years ago. And in that time, I've been round to all three of the sisters houses. We have spend christmas together. Gone to Portugal with the brother-in-law (and his wife) in question. Been to restaurants together, done everything that people that are friends would normally do.
It's a shame that it is coming across like I am not making an effort to show that we get on well as a couple.
As for her other sisters, I have no problems with them. As I said before, the girlfriend had said that *someone* in her family didn't approve. But didn't want to tell me who. But I didn't make a fuss about that and took the view that the girlfriend had. Two years ago. Their opinion is their opinion.
But most importantly, I have not, NEVER WILL, and don't expect my girlfriend to choose between me and her family. If I have implied that anywhere, please point me to that passage and I will edit accordingly.