But - will you just go kill him without even calling the police? Without even trying to get him jailed? If so - think about the Mc Martin preschool case, and Dale Akiki. Dale was a nice, wonderful man, weird looking, but dedicated to his children. He was arrested after a bunch of them made accusations that he was molesting them in the most horrible ways possible. Not just one child, several. Had you killed him based on that, you'd be wrong, you'd have killed an innocent man. The problem was a psychologist who lead the children, used hypnosis and several other techniques that generated false memories - with the best of intentions on his part, the childrens part, the parent's part, an innocent man was falsely accused, jailed, and tried. At trial, everything came apart - the stories were inconsistient, impossible, and denied by children in the same room as the supposed acts who were not 'helped' by that particular psychologist. Pretty much the same story for McMartin.
I know, all parents believe their children, believe these things happened, especially when more than one child says so, but even if it was only their child. But even without any malice, there can be horrible mistakes, and jumping the gun to go kill someone without even giving the police and the courts a chance is wrong. In this case, it sounds like she probably got the right person, but it isn't a good thing to let go. And sometimes there is malice - misidentifications because the child is too afraid of the molester to name them; divorce cases where a parent uses false accusations to try for better custody or just to hurt the other person, etc.
He probably did it - but we'll never be sure. If the police refused to do anything, then she has no other choice but to take it into her own hands - but that doesn't seem to be the case here.