L.R.
Some people just prefer friends to family. Accept that your SIL is more into friends than into you. Being relatives doesn't obligate you to be her friend, or her to be yours.
Do you really want her friendship, or do you feel more that you simply expect her to do things with you and invite you over and see you often because she's family? In other words -- if she were not married to your brother, would you really, honestly pursue having her as a close friend based on her own personality, interests, and character? Think hard about that. If you only "generally like her" as you put it, but would not pursue her as a friend if you just met her somewhere and she was not married into the family -- then don't sweat it so hard that she's not putting you first.
Find your own friends, catch up with folks who share your interests and hobbies -- not just those who share your family ties.
If you are sore at the thought that she is getting so close to this woman whom you dislike and whose character you have issues with: You can't control that, and if you go to SIL and try to say, "This is what this woman's really like," SIL is going to choose the friend over you and you will come off as jealous and gossiping, even if you are truly not and are trying to warn SIL. I would leave it all alone. They are adults and you can't change or control them; you can only control your own reactions.
Invite over some other couples you know. Have friends over for a dinner or barbecue. Get to know parents of your kid's friends (or if your child is very young, get to know parents through play groups etc.). Don't waste any more energy on wondering and worrying over "they don't have us over, don't try to go out with us, don't call us." It truly is a waste of energy you can put elsewhere.