I've lived with an anxiety disorder my entire life, so for me those stories and images just "loop" over and over again until I can't bring myself to take my children out of the house for fear that something will happen to them. Since it's not fair to keep them cooped up because of my disorder, I've come up with several coping strategies. Hopefully they will help you as much as they've helped me!
1.) Remind yourself that these crimes are largely committed by people who know the child. A desperate mom who sees the child as a barrier or has to work and feels like she has to leave the child with an unsafe person. Or "falls in love" with a "great guy" who neglects to tell her about past charges, etc. If you're financially stable and provide a loving home and are careful about who cares for your children, their faces won't be on the news.
2.) Look at whether you're reading national or local news. If you've read five bad stories in a row, was that five for the country? Five for your state? Five for your city? And of those, how many were random crimes and how many were perpetrated by someone who knew the child? If five random acts of violence against children were committed in your city, worry. If not, say a prayer for the children affected but that's all you can do. You can't change the outcome.
3.) Get your news online. If you see a headline about one of "those types" of stories, don't click on it. Having ALL of the details only enhances your imagination and helps you put the faces of your own children into the story. All you know from a headline is that a child was hurt. Say a prayer for the child or children affected but that's all you can do. You can't change the outcome and knowing the details of what happened to them won't help anything.
4.) Take action. The only way these stories will disappear is if we donate money and time to the organizations that help them. Even if we can't prolong their life, ultimately we will have made the time they had here more bearable and given them at least some of the joy they deserve to have. And if even one life is saved, wasn't it worth $20 and a few hours of sorting toys, pushing swings at a community center, or donating books?
Praying this helps!