There are other, simpler, less elegant solutions, but in order to set this up the way you want it, where moving between access points is completely seamless, you will need routers which support wireless distribution system. Essentially the way WDS works is that each router is configured with the same radio channel, encryption scheme, and (for usability's sake, though not technically required) SSID. One or more base stations is connected by ethernet, and then repeater stations rebroadcast that signal. Clients can move back and forth between access points transparently; you will automatically connect to whichever is closest. You will need routers which are compatible and support WDS for this to work.
This question has already been discusses in Buying another router and use as a "signal repeater" in bridge mode?. That information will likely solve your problem.
– nhinkle – 2010-12-18T01:59:37.9971@nhinkle, not quite the same question. The OP has ethernet in both rooms. – heavyd – 2010-12-18T02:05:36.183