The place to dissolve your anxiety is by becoming aware of the thoughts you are having and questioning them. You may be thinking that you "should" be able to protect your children. Or that being a good parent means that you will always protect them. In light of the world we live in, these are impossible scenarios. Whether we should or shouldn't we cannot protect our children and it does make us feel a little crazy to think about trying to.
Instead focus on all the things you have within yourself to deal with a crisis/tragedy if it were to happen. We don't usually make ourselves really aware of our inner resources. What are the things that you have within you that have allowed you to make it through the tough times you have already faced in your life? Are you creative, intelligent, street wise, tenacious, determined, focused, kind, generous, empathic, organized, etc. What are the specific tools and skills you have that you could bring to any disaster? Can you cook, plan, do CPR, manage people, negotiate, tell stories, have a sense of humor, see the big picture, hug, be gentle with someone that is frightened or anxious?
Too often we allow the thoughts in our heads to run away with us and dwell on the worst possible scenario. The way to get through that effectively is to ask that thought "Then what?" You continue to ask "Then what?" till you are years down the road from the imagined disaster. Life always goes on no matter what. We have a tendency to only go to the imagined disaster and dwell in the middle of the pain of the disaster rather than follow the thought process all the way through.
Horrible things happen every day. How do we get through? How do we go on? What does life look like down the road? Of course we don't want these things to happen, however, as long as you simply dwell on "This shouldn't happen!" you will suffer. Instead, look at "What would I do?", "What have I done in the past?", "What have other people done?", "What resources do I have?", "What resources might I need?"