Well first off I have to admit I don't live where mountain lions are, so it's easier for me to say this. We do have coyotes outside of the city; I know some of my friends have been approached by one or two when out walking with their kids, and I know it was scary for them.
I am a wildlife rehabilitator, and we handle about 5,000 calls each year about wildlife questions. Whether it's bear, deer, mountain lions, skunks, there is always questions about children getting hurt.
And of COURSE it's a concern.
That said; I wish there was an answer. But we have encroached upon all wildlife's homes. There really is very little land for them to call theirs, and when they come too close to "ours", it always causes upset and most often results in harm to them.
Of course if there are rogue mountain lions coming up to people, something has to be done. But just because they are there doesn't immediately mean they are going to come and get everybody.
If you look at your city's statistics about children in car accidents daily, I'll bet you lunch for a year that there are many more kids injured in cars every day (or by other people ie: family members or friends) than any mountain lion would cause.
Here is some reading material on the subject. I don't know where you live, but it's good advice no matter where you live.
Here's another, just for the heck of it.
The big thing is to make sure you never leave food (or small animals) outside unattended. And make sure your neighbor's don't either. One of those sites said that people intentionally feed the lions - that is
crazy.
Ihope I am not coming across insensitive to your concern; if course it is unnerving, but I just thought some reading material might make you a little more at ease.