Overall, there are a lot of different options for doing what you're doing, and which to choose depends on how much money you want to spend vs. how much effort you want to put in yourself to custom-build a solution. There are also performance and power-usage tradeoffs for various solutions.
Here's one quick and cheap solution: If you're fine leaving your computer and directional antenna where they are, and you're fine leaving your computer on all the time (and I mean really on and running, not in sleep/standby mode), then you could just enable your OS's version of Internet Sharing to share from the one Wi-Fi interface to another Wi-Fi interface (get ahold of a USB Wi-Fi adaptor), which you'd put in "Software AP" mode on a different channel. This is cheap in terms of new hardware costs, but comparatively expensive in terms of electricity costs. Having a full desktop PC running all the time takes much more electricity than a small energy-efficient embedded processor in an off-the-shelf "Wi-Fi Range Extender" box.
Just have to ask, are you allowed to be connected to the network "across the street"? – Paul – 2014-02-05T18:15:39.603
1Yes. It's my family. I pay part of the bill. – Peronix – 2014-02-05T18:16:15.063