Farm Works will run on a network. However, there are certain files that will need to be installed onto the hard drive of each machine on the network. The easiest way to insure this is to install Farm Works from each machine into the same directory on the common network drive. The only drawback to running the program on a network is that it has not been designed specifically for networks. What this means is that you should not have two people working in the same project at the same time.
Other than running on a network there are no ways to "merge" data from two different computers. You can exchange data via backups from the two computers. However, whenever you restore a backup you will overwrite the current information completely with the backup.
If both brothers had e-mail the best bet would be for one brother to enter his information, then e-mail a backup to the other brother to enter his information then e-mail it back. The only thing about this is that after one brother e-mails the backup to the other, he can't enter any information into the computer until he gets a new backup from the other.