Hi The-Pro,
I'm not sure precisely what you wish to do, or why, but allow me to suggest a couple scenarios:
(1) Perhaps your Mac mini server is in the closet and thus you cannot easily attach your iPads and iPhones to it for syncing, thus you wish to sync your iPhones and iPads via another Mac?
Well, under the latest iOS 6, you can now sync your iPhones wirelessly, so you may be able to do the sync without having to physically attach your iPhones to the Mac mini.
Or on your Mac (not the Mac mini) running iTunes that you use to sync your iPhones and iPads, you can pick the iTunes Library on the Mac mini using the "Choose Library..." option. This means that you Mac's iTunes is loading the Mac mini's iTunes Library that has all of your media in it. You then sync your iDevices attached to your Mac to your iTunes Library on your Mac mini.
(2) You wish to clone and update your iTunes Library on your Mac mini onto your Mac.
If this is what you wish, then use the "rsync" Terminal command to keep the iTunes Library on your Mac in sync with the iTunes Library on your Mac mini.
Regards,
Switon