Well, remember to the Arduino place in a safe and fixed position in the house (for exaple fixed on the roof or fixed inside a electrical box on the wall) because if someone will open one of the doors connected by wire, our goal is that the wire will be disconnected from one of the two used Arduino digital pins (in order to open the controlled signal circuit).
Now, let’s go to code some line. The ultrasonic sensor is managed by the excellent newPing library, and the code to send email using the Arduino Ethernet shield is took from the my preferred site about Arduino resources (the only and one Arduino.cc …”made in Italy” rules! :-)), and modified by myself. The specific link is the following: http://playground.arduino.cc/Code/Email.
So, this is the code.