If you can't make any changes, here's what I'd do.
Pick out the most reliable person, and let them know of this plan.
As soon as you know the gate for the onward flight text the gate number to that person.
Tell them to look for a text the second they land.
Tell them to text you as soon as they've landed and have access to their phone so you know they're in DEN.
You should wait by the gate for the ongoing flight, and engage in conversation with the agent. Let him or her know that 14 people are hoofing it over from flight xxx at gate yyy and they're on the ground.
If time is really tight watch for the kids and let the agent know the second they're in sight.