This is a tricky one, because it's hard to know MIL's intentions. Regardless, I can totally see why this would drive you crazy. Here are some options, and you can see which fits best for your personality.
-Be fairly direct. If she cuts you off or starts in on one of her stories, simply say "oh I'm sorry, MIL, I wasn't quite done with what I was saying, can I finish?"
-Stop sharing as much. When you feel her coming on with this behavior, just check out. Wait until she takes a breath, and then excuse yourself or start talking to someone else. I don't see this as being rude or passive aggressive, it's a survival technique. I personally don't like confrontations, so doing the first thing I mention would not likely happen. My option is to just take myself out of the equation. There are other people I can share with, it doesn't have to be her. Impart the info she needs to know about her son and grandkids and that's it.
-To move into passive aggressive territory, if you stop sharing much, and someone else mentions something, she might say "oh I didn't know you were doing x,y,z" and then you can say "oh, I think you missed it because you were talking about your x,y,z". This will let her know the score.
You will get a lot of advice about what to say, but if it doesn't fit your personality, it won't matter.
I will also say to maybe give her the benefit of the doubt. Why do you think she is like this? Maybe my story will help. My mom, who is the sweetest person in the world, does this. It makes me crazy. If someone is telling her a story, she doesn't interrupt, but instead of asking following up questions or being really interested, she finds a connection to her life and goes on about that. It does bother me, because if it was anyone but my mom I would be complaining. But I also know that growing up no one paid much attention to her. Then as an adult she always felt kind of insecure. So for my mom, she does this to be heard, and to feel like she matters. I try sometimes to gently mention that she may want to listen more than she talks, and she'll try, but it doesn't last. I can't change her. So I just have to love her for the reasons it has come to this. And then complain like crazy later! Or try to rescue conversations as they happen and facilitate more back and forth.
I don't know if your MIL is more like that- a nice person who just has deep reasons that she needs to feel important, or if she just thinks she is better than other people and likes to prove it. Only you have the best guess for this. And the answer to that should help guide you. But ultimately you can change your relationship to suit you and keep you sane. Not hate her or cut her out, but expect less understanding and listening ears from her.
Good luck. I know it's hard to deal with people like this, whether innocent motives or not.