How old are your children? Can you give the oldest a prepaid cell phone with the home number already in it?
that way should things become 'strange' or 'odd' or making the child 'nervous' he/she could at least call home and let you know and then you could go from there?
My oldest granddaughter was given her 1st cell phone at 7 years old, only to be used in emergencies with both her home phone and gramma's number (me) programmed into it. She only used it twice those first few years, understanding what it was for, but we were right there in a hot minute.
Just a thought, and it would probably ease your concerns a bit, knowing your children had a way to reach out to you.
Love and hugs,