You are not really using the same library. The library exists on the individual computer, not necessarily just in the iTunes login. You can log into the same iTunes account on both devices, but the computers identify the libraries as different, they have a unique ID. That is how iTunes know the device is synced to a different library. Also, if you are syncing music, you cannot add a few tracks from a different computer, without telling it to sync the rest of the music as well. That is how syncing works. If the library at Dad's house is exactly the same as the one on the computer at Mom's, you could go ahead and sync. While it would delete all content, it would then sync it back, if you have the exact same music in each library. However, eventually you would have a problem when you keep overwriting the libraries like that.