This is probably the most annoying limitation of Trados freelance: two copies cannot run on the same network, even if you have paid for both copies. SDL wants you to buy a pro license.
According to SDL’s the reason is that running two copies of Trados at the same time is something only an agency would, and they want agencies to buy the more expensive pro version. So, if you are not an agency but you live and work with another translator, you are out of luck: you can either run Trados on two disconnected computers (so you cannot share a fast Internet connection), or you can have both computers connected, but only one of them running Trados.
There is a way you can still share the same Internet connection without violating the terms of the freelance license: put the two computers on different networks.
The way I’ve done it is by adding an inexpensive wireless router to our wired home network.
Our computers and various devices connect to our Internet router via Ethernet cables. Also connected to the wired router is a wireless router, to which our laptops can link. When it is time to launch a second freelance copy of Trados on one of the computers, I just unplug the Ethernet cable from my laptop. At that point the laptop is no longer on the same network as my partner’s desktop PC, but it still accesses the Internet (through the wireless router).
This is just a workaround and still a nuisance (the physically disconnected laptop no longer reaches some of the peripherals). I suspect that I could find a better solution if I knew networking better, but this is a useful stopgap: this way we can have two copies o Trados running at the same time, from two computers that share the same Internet connection.
Read the comments for better way to sidestep this issue. Also, as Paul says in his comment, SDL finally did the right thing, and this issue no longer affects SDL Trados Studio 2009 (the newest version of the program).
One thing I did not mention before: we do have one copy of Trados 2007 pro installed on my desktop PC, so normally this old Trados issue does not affect us - my wife works on her licensed copy of Trados freelance, and I on my licensed copy of trados pro. However, we also have a second freelance copy installed on a laptop, for use wen, for example, I work offsite. Right now, however, my desktop PC is out for repairs, and I have to work from my laptop, so I was forcibly reminded of this really annoying Trados built-in limitation.