I'm willing to bet that if after that much time you haven't developed a close friendship with your SIL, that it's not going to happen. Is she polite and respectful to you, but just not close? You admit you had expectations for her, but she has no obligation to fill them. There is nothing you can do to make someone have a close relationship with you if they are not interested.
My answer would be to focus on your relationship with your brother and leave your SIL out of it. If he wants a closer relationship between you, your FOO and his family, it's his job to make that happen and maintain it. It's also entirely possible he's ok with the way things are, and pushing him or her for more may backfire. My MIL wants a lot more of our time than my DH is willing to give even though he knows she's not happy about it (and I get the blame for it). Her being pushy about didn't do the relationship between her and myself any favours.
I have a good, but not close, relationship with my SIL. I am and always have been open to having a closer relationship with her, but I know that it has to happen organically, and neither side pushing it will help. We recently suffered a family tragedy, and I can say I've gotten much closer to my brother and his family as a result, but it's through my brother that that has happened, not my SIL. He is happy, and she is supportive of him, a great mother to their kids, polite and respectful to our family, and that's really all I could ask for.