I noticed that if I use ip references for my connected systems as opposed to network names, the mouse behaves much better.
Interestingly, when playing around with the layout and settings, when I tried to change one system from an ip address to network name, InputDirector told me that the computer was already represented by another (different) named machine. It seems that either my network is troubled (which I haven't noticed until this situation) or InputDirector is having trouble using network names and assigning the appropriate ip address.
On my network, my router assigns ip addresses based on the MAC addresses of each computer. The ip assignments are always the same and predictable for each machine. The same router assigns a name to each respective machine. So I'm not sure why InputDirector gets confused.