I like your boxing idea. I think that will have the most immediate impact. It won't take long for her to be punching hard with great footwork and balance. Plus, light sparing will get her used to dealing with incoming strikes and realizing that the incoming punch doesn't need to miss by much to be completely ineffective. It's also something that she could do by herself with a heavy bag and/or one of those cool "Bob" punching forms. I bet you could find some former boxers in your area who would be willing to train her on an hourly (or 1/2 hourly) basis.
Brazilian Jiu-Jitsu is great too but for different reasons. It takes a little longer to feel competent but it has the advantage of being a group environment which would offer her a different, positive, peer group.
MMA may be a blending of both. Maybe you can both train together? But don't take self-defense advice from me:
As a parent, you're doing the right thing by trying. When my son was younger (like middle school through high school) I used to say that he never wanted me less but needed me more. (My daughter was much easier.) I think the point is to try to get girls to about 22 years old and boys to about 30 years old without them having made any life-alteringly stupid decisions. For some people, parenting is smooth sailing, for others it's maneuvering through one storm after another. Our kids are not "our" kids after all. They are their own, autonomous humans. Control is an illusion. All we can do is be indefatigable and have the "I love you and there's absolutely nothing you can do about it." attitude.
My daughter was my first born and when I first saw her I realized that from that day forward my heart would be wandering around outside my body for the rest of my life. It's stressful at times but it's what you signed up for. You got this.