Sorry I don't have the answer (have to manually mount it or add to login items) but I'd like to know if there is a way too. It doesn't make sense to me that it wouldn't do this automatically. Can you check to see if your daughter's Mac has it in login items? Or perhaps a script she wrote?
Someone suggested that the TC drive can be permanently mounted by going to the finder, and clicking "Connect to a Server" in the "Go" menu, enter the TC's IP address, and it should mount. I just tried that now, and it mounted successfully, but im not sure if it was permanent as I have yet to restart. Ill see if it worked tomorrow.
Assuming you are on 10.4, you are looking for software called Airport Disk Utility. Its included on the disk that comes with your TC. Here's an overview:
When I type in both the IP address manually and click Browse, nothing comes up. Browse finds nothing, typing in manually says The Server may not exist at this time or is not operational at this time.