unclemoosh, I think that cable is exactly backwards to what I need. As for handshaking, there's none involved. With weather stations. Data goes one way, and that to the computer.
That may be true for some stations, but not for Davis. The computer asks for specific data from the station's logger, which then sends it back. It can also send commands back to the console, set the clock, turn on the backlight, set calibrations, and more.
If the station does, indeed, stream data continuously, then a splitter should work. I've used B&B Serial Datataps for this. They have a set of dip switches for the tap port that allow you to control which lines are connected. That may be preferable to a Y, where handshaking pins from each computer will be connected to each other. Or, buy 2 cheapo serial cables and build your own. If you have trouble, it could be ground loops between the computers.
Have you considered trying a software splitter like Xport or GPSgate? They've been used to split data streams like this before. The app talks to the hardware port and then repeats the data to 2 or more virtual serial ports, kinda like VirtualVP for the Davis. Then you can run both programs on one computer.
You could test how the station works by connecting to it with Hyperterminal and watching the data stream out of it.