This is very clearly a bug in Yosemite given that it began for most people when they upgraded to Yosemite. I realize that this happened on a small scale during previous Mac OS X updates, but not to the extent it's happening now.
If you have a computer where file sharing has to be turned on and where "wake for network access" has to be turned on, my best advice is to either wait for a fix from Apple or else reintstall Mavericks--not an easy task because you must wipe the disk, reinstall mavericks and then use Migration Assistant to bring over your apps and data from your previous install. We have a home media server (an older MacBook) and I got so frustrated that I did reinstall Mavericks. And that was a 100% fix for this problem.
If you can turn off file sharing and turn off wake for network access on the problem computer, that MIGHT work.
Also, if you have an Apple Airport Express or Airport Extreme where that device is providing your local network, open Airport Utility and click on the device picture and then click "Edit." In the Base Station tab, add your iCloud ID towards the bottom of that window. Then click "Update" to update your Airport device. If you have multiple iCloud IDs that are accessing the shared computer, do the same thing on each of those computers. That MIGHT also work.