It is a safety issue while driving.
Nowadays, I don’t stop if I see someone broken down on the side of the road, as I assume they have a cell phone and can make their own call. If cell phones weren’t common, I would stop. I feel the risk of stopping with little kids when the chance of the person NOT having a cell phone, is not worth it. Even if the people are frum.
When my tire blew out on my car, I was able to call AAA, my husband and my friend who I was driving to. If I hadn’t, I might have been stuck on the NJ Turnpike on Shabbos. You don’t think a woman alone, stuck on a highway, is a safety risk?
As to trusting your kids – monitor their usage! Disable internet if you would like (its disabled on my phone). Don’t allow texts or minimize amount and who they can send to. And most of all MONITOR them. Trust but verify.