I guess that at least the door switch part is to powered by battery.
Anyway, even if not, probably the best configuration is to have the ESP8266 which monitors the door switch configured as a web client. When the door switch changes state, it wakes up and posts (using HTTP POST or HTTP GET) the status update to the web server (another ESP8266). After that it goes back to sleep. The ESP8266 configured as a web server must run all the time, waiting for status change messages from the ESP8266 monitoring the door switch and act on them issuing alarm calls etc.
If you have an existing wifi network, then it is probably best to integrate the two ESP8266 devices in your existing wireless lan. If not, you can make the ESP8266 which is designates as the web server also into an Access Point (AP mode) which effectively creates its own private wlan.
The mechanism is simple. It is exactly analogous to using your web browser to post a message in this thread. Your browser is the web client and at forum.arduino.cc there is a web server running which accepts your post.