Hi, sorry I don't have an answer for you but I can sympathise because since I had children I also experience this along with some self generated intrusive thoughts which have the same effect. I hate it, makes me feel I'm not in control of my own thoughts, or else just too fragile too cope when this is not the case.
I can share a few ways that I've approached it:
I kept a log for a few days and found that for me it was linked with being tired, eating too much sugar/caffeine, between 8am-9am or 3pm-6pm (no idea why), and being on the computer too late the night before. So this gives me a chance to control it a little. Have you noticed any patterns about when it gets better/worse for you?
I find mindfulness meditation helpful to see the spaces in between the sad feelings (sorry if that makes no sense).
I remind myself that this is one of those things that probably made evolutionary sense in a wild environment - i.e. being hyper sensitive to threat would make you a great protector of the young in the community. This helps me deal with the fear about things happening to people I know - when I get those thoughts I remind myself that it's just a rather horrible misplaced alarm bell to go check on the kids, for example.
The overwhelming sadness is tough. For me it is linked to feeling helpless about the suffering I see, and it kind of paralyses my mind so I get stuck on that sadness. It helps me to take action in some way: deliberately be kind to someone, say a prayer, donate to charity, help someone at work - it all counts. I try to remember we're all connected - eventually, someone I help could help someone who helps someone who cures cancer, for example. Sorry, that sounds a bit rubbish and trite when I write it, but it works for me.
Hope this helps, sorry for rambling.