Summary: I'd like to use two Ubuntu computers to extend/compliment an existing wireless access point.

I have a network which currently looks a bit like this:

What the diagram doesn't show is the interference caused by our house. It's a wifi-blocking robot sent here from the past. The two wired computers are in areas where the signal is most blocked (not by design, just a happy co-incidence).

Both wired computers have fairly good network cards. They're both Ubuntu machines and I would like to turn them into additional base stations.

I know I could throw more networking hardware at this (network extenders or cable in additional, pure wireless access points) but I've got two Linux machines sitting in ideal places and I feel like they should be able to help me out.

I've tried ad-hoc networks but I need something that is a lot more transparent (eg you can migrate from base to base without a connection dropping); it should look like one network to clients.