Bock, welcome to CNet's help forums in general and the Speakeasy forum in particular. Typically here in Speakeasy we mostly ramble and rant about sex, politics, and religion - all the things we aren't permitted to discuss in polite company...
While the techical forums are probably better places to get an answer to your specific question, let me give a few observations from my experience with WLANs. I feel your pain with the spotty signal in a distant part of the house, however my personal advice is don't put a second WAP in. Multiple WAPs (including the "range extenders") on a network are technically feasible, but you have to work at keeping the coverage zones from overlapping too much. When a client system, particularly one running Windows XP, is in a spot with more than one reasonable signal, it could get confused about which access point it should tune to. With the XP zero configuration utility running, your system will disconnect and reconnect every minute on the dot as it polls the several available signals trying to decide which is the strongest signal - not a pleasant sight if you are trying to maintain connectivity for even casual web surfing.
If I were in your shoes, I would cough for the CAT5 wiring in the new house while the walls are still accessible. Wireless is great, but it is limited both as to coverage (which you've already experienced) and as to network speed, which you may not have noticed because even the slowest wireless transfer rates are faster than typical DSL or cable modem speeds. However, if you ever want to transfer large files between computers in the house or - and this is still very futuristic - start transferring multimedia (video and audio) from one part of the house to another, you will have much better results with the wired systems. If you can, put the infrastructure in place now.
Finally, back to your original problem of spotty coverage... For a few dollars (or even free if you have some of the right stuff just laying around in your garage...) you can boost and focus the signal strength of your current wireless unit. Usually, with a little tweaking and repositioning things slightly, you can penetrate those dark zones. Here is one article that may help.
Hope this helps, and welcome to CNet.