if the cordless phone base is right next to the airport base, then those signals are competing with each other, and being blocked by the same walls. While the signal from the other house might have a straight shot.
try unplugging the phone base and see if your reception improves. there are 5GHz cordless phones that will not interfere with 802.11g (which runs at 2.4GHz) although you could run into problems if you try to upgrade to 802.11n
Where is the extreme located? buried on the floor behind metal computer cases and furniture? it's best to have it free from any obstructions, and i've heard that higher is better, so up on a book shelf with lots of airspace around it is best.
also most antennas are directional, so if you've got the extreme on it's side, your shooting most of the signal into the floor and the ceiling.
draw an imaginary line from your router to the computer in the other room, what does it pass through? mostly air? are there lots of things (particularly metal) like file cabinets or furniture that it passes through?
wireless is not an exact science. due to the way we live now, wireless interference comes from everywhere. No two locations are the same due to things like outside signals, building construction, and other obstructions. so what works for someone else, might not work for you, and there is a chance that wireless won't work at all in some situations.