I have a similar setup - 5 iPhones, a couple of computers, iPad, etc.
I have the masters on my Pro - it's always on and powerful enough to keep iTunes and iPhoto running in the background.
Each user has their own iCloud account for email, calendars, etc.
We share a single family AppleID for purchases - this is setup on each device for Music, Videos, and AppStore.
Given that all music, videos etc are bought using the same ID, when they're bought on a device they sync into iTunes on the central library Mac automatically. Each device can optionally turn on downloads of purchased items from other devices. That's a per device setting.
Each user controls their own iPhotos - this isn't a problem for the kids. Between my wife and I, put our own photos into our own iPhoto libraries. Both are shared, and we can drag and drop between them as needed within iPhoto. This doesn't sync automatically, but it's easy to tell on the event level what needs updating.
Home Sharing allows all devices to play whatever music and videos within the houses' wifi network, including on the AppleTVs. HomeSharing also (at least used to) allow for automatic syncing between devices to keep everything on one account, if added outside of the store. With laptops for the kids, they can keep their own smaller libraries and stream via HomeSharing in the house, and copy to their own accounts to store stuff for outside the house.
Outside the house because we're using the single account, everyone can play any music via iTunes Match. With the latest Apple update, this now includes movies and TV shows bought through iTMS.
I like to connect devices with no visible display to iTunes and see that I can make a backup of the device. At that point, I follow the 6 step process (even if I don't think the first few will work, sometimes going through the shutdown motions revives the screen.)
If you can make a backup, you have a good base and then can try a restore. Also, if you haven't powered it off, that might do the trick without needing a computer.
Best Answer
No.
If you could simply override the setting from the computer, that would defeat the purpose of iOS not exposing internal data until it has been approved through the touch interface.