Look on-line for places that sell the same kind of fire/burgler alarms that are usually installed by alarm companies to homeowners. Personally, I bought an "ELK M1" along with a receiver that picks up signals from the Honeywell/Ademco alarm sensors and panic buttons. The programming model for these is a bit arcane, but they are rugged and reliable.
You can set up a smoke detector to automatically call a monitoring center (less than $10/month) and have them send the fire department and you can similarly use all of the standard burgler or adult-panic-button features to call police and medical help. This is all very configurable.
For your child, you can program the child's "look at me" button as a "Non Alarm Zone" so that it doesn't trigger the alarm immediately but causes the system to call you (or text you or email you) or take whatever additional action you want. (In my case, I also added a Universal Devices controller that does even more automation stuff).
You also may consider having the child's button trigger an actual panic alarm after buzzing for a while in the house. So, if the child hits the button and neither you nor your wife cancel it, professional help would be called.
Many of these systems are very configurable and a good monitoring center can have special instructions for different alarms (call house, then call you, then call help). They are a pain to program (designed for non-programmers) but surprisingly flexible.