Linksys Wireless Router :: Wrt320n Building Home Network With Wifi Roaming

I live in a new apartment building which means a lot of concrete. The internet (fiber) enters the house at the beginning where the modem is hooked up to my Linksys WRT320N. From there two cables run through the house:1 to the home office, where two computers are connected through a switch.1 to the living room, where the Xbox, blue-ray player are connected through a switch.I also have a wifi network running from my WRT320N, but as it is at the beginning of the house, there are some black spots in other parts of the house. I tried to fix this with a Netgear repeater, but that keeps disconnecting.
 
What I want to do know is place a second linksys device in the living room at the end of the already existing cable that will also broadcast a wifi network, but I want this to be exactly the same Wi-Fi network as I already have. What I want to achieve is that I can walk from one end of the house with my iPad, streaming a video, to the other end of the house and that I always stay connected to the internet and that my tabled just picks up the strongest broadcaster, basically the same as with a mobile phone.