Scenarios like this always run through my mind when I'm out with my kids. (And alone.) I don't want to end up being one these stories so try to be prepared and mitigate as much risk as I can without sucking the fun and adventure out of the the trip. So far so good, but it doesn't take much for things to go South. I'm glad this one turned out well. Kudos to the SAR team!
FWIW, most of the trails in our area were beaten up pretty badly this winter. There are trees down everywhere and lots of flooding to navigate around. In addition to a high risk of mechanical injury, it would be so easy to get turned around. Most signage is poor, with signs and blazes knocked down by the rough winter. It would be very easy to get lost if you don't stay on top of your navigation, even in a small park. As I said to bacpacboy after we came across another downed sign and blaze on a weekend hike, it's always smart to use a map and compass.