Some times it's easy to get locked into one mode of thought - that's what happened to me on this. I helped someone install a series of web cams in his house that connected to a video server that streamed video to a web server to which he connected. There is an easier way.
Most of the instant messaging clients, such as Windows Messenger Live and Yahoo! messenger, have the ability to create a connection between computers and web cams. To use it, you and your mother would have to have the same IM client. For example, if you both have the Windows Live Messenger (which I've found to be more stable than Yahoo!), you can enable web cams in sessions.
The upside is that it's simple. Connect the web cam to the computer running the IM client. Then, simply connect to your mother's computer. Click Options - Send Video, and select the web cam as the source. The web cam should come with all the hardware - it's just one cable. The software is bundled with it, and installing it using the defaults will work just fine in most cases.
The downside is that both of you have to be at the computer and "on-line" on the IM client at the same time. Not a problem if you set a schedule or just call to be sure. The other downside, though, is that you have to take the baby to the web cam, rather than installing the web cam near the baby (although you can do the latter - you would just need a cable long enough to run from the crib, say, to the computer). The other downside is that since you are running it to a web page, the only way someone can see it is if they, too, have the same IM client, etc. And, of course, your mother has to be able to install and operate the IM client.
Anyway, that's a much simpler way of doing it, but it is more limited in application.