What exactly is this "network-extender" and what is the "livebox" ? you wrote the netwwork-extender is connected to the livebox by cable. Does the network-extender have WiFi?
You have to provide more details. Best thing would be download-links to the manuals of each part that is involved
Livebox is an ADSL wireless router available to customers of Orange's Broadband services in the United Kingdom, Kenya, Guinea, France, Tunisia, Spain, Jordan, the Netherlands, Switzerland, Poland, Belgium, Orange's Mauritian partner MyT, Lightspeed Communications in Bahrain and Orange Botswana.
@danielpsk: the WiFi extender should extend the range of your Livebox WiFi so there should not be any changes required in any of your sketches. But this may depend on the extender I guess.
Another possibility would be to use an additional ESP8266 module in between the 2 others. Then use the PainlessMesh library to create a mesh network that enables the 3 ESPs to communicate.