Instead of backing up the disk, one could also easily rotate the external disk. Time Machine will always continue where it left of for the disk that is connected while running a backup†.
To (initially) clone an existing backup disk, see "Mac OS X v10.6: How to transfer your backups from your current hard drive to a new hard drive" in Apple's Mac 101: Time Machine. (Copy preserved here.) Beware:
If you see sparse bundles then you'll need to copy those as well. Those are the backups for the MacBooks, if they use the backup disk while it's connected to the Mac mini.
I don't know, but it might be important that Apple writes about using drag & drop. A regular copy in Finder or Terminal might mess up with the hard links that TM uses. Or, maybe 10.6 handles hard links much better than 10.5 did. Apple's instructions might not work for 10.5.
Steps 10 and 11 in that Apple article explain how to tell TM to use the cloned disk. I'm not sure that is actually required; it seems that following Apple's instructions will copy the full backups, including the hidden "cookies". So, skip 10 and 11 and see if TM is willing to use both the old and new disks without you explicitly telling TM you swapped the disk.
If TM does not want to use both disks without you manually changing its settings, then if you're in for a Super User answer, then steps 10 and 11 can be replaced by making TM oblivious that the connected disk has changed. For that, ensure the "cookie" for each backup matches:
On the backup for each Mac, find a hidden file named
.aabbccddeeff, its name matching the primary MAC address of that Mac‡ (in Terminal, see the output of
ifconfig | grep ether). For the Mac mini, it's probably in a folder
/Backups.backupdb/name-of-mac-mini. For the MacBooks, the backups probably use sparse bundles, which also have names that include the computer name and its MAC address. You'll need to open/mount (double click) each sparse bundle first to find the hidden file.
Set the contents of that file to match the contents of the file
/var/db/.TimeMachine.Cookie of the Mac that belongs to that backup.
Presto: swap the backup disk whenever you want!
This works because TM stores the last known so-called event ID with each backup. So, TM does not rely on information on your Mac to keep the backup disk in-sync with your Mac. After swapping disks, this event ID on the new disk will be lower than the event ID used by the previous backup, and TM will know it needs to back up a bit more than last time. In fact, TM probably doesn't even know what event ID it used last; it will always fetch the last used value from the backup disk when running again. (The event ID is stored in the extended attribute
com.apple.backupd.SnapshotVolumeLastFSEventID. Ars Technica features a well-known technical article, explaining how TM uses the logs maintained by
When doubting the above: use tools like TimeTracker to see what is written to the backup.
‡ Incidentally, using that primary MAC address is also the reason why existing backup disks might not be recognized when you get your logic board replaced. The logic board seems to include the AirPort network adapter, and hence replacing the logic board will also get you a new primary MAC address.