Max number of registrations from same OSX install disks

If you are booted from the second installation, so it can look for its
own Software Update online, it should be able to find them. Also,
you could re-install stand-alone downloads of the updates, offline.

{You may have to be booted from the OS X restore/install DVD
for the computer, in order to have it choose an external drive
choice, but you should also be able to choose a destination drive;
perhaps with different rules depending on where a 2nd HDD is.}

The 'registration' of an OS X version, if you have no internet, or
use offline update downloads of the necessary files; isn't needed.
So, you do not need to actually 're-register' but you do need to
run the Setup Assistant and personalize the computer, even offline.

(However, you would have to *personalize a new installation* and
that setup is where you get into a 'registration-like' mode. You
can choose to not go online, if you already have all the files on
DVD or CD from a previous standalone download of each.)

While a single-user OS X retail install (and the machine-specific
computer restore/install disc system) is licensed for one-install,
you can make a Clone of the system and use it for backup; this
also helps when you can boot from the Clone in a supported 2nd
hard disk drive and use one system to help fix another.

You do not have to register an OS X system for it to function. It
can be used offline all of its life, and do so just fine. You can go
elsewhere and get the stand-alone update files from the internet
and save them to a USB thumbdrive or other portable storage,
then apply them with the main computer offline, over & over.

So, I guess I don't understand the question. I make and use full
clones of everything in my computers, so essentially I have two
boot systems for each one installation; one is a complete copy.
For making a Clone, my preference (due to experience) has been
to get and use Carbon Copy Cloner from Bombich Software online.
It runs free, though is a donationware; and info is on their web site.

A clone is nice, if you can make more than one; an initial clone at
the point you first install a new system and update it; then a later
clone with your Mac's current complete hard disk drive, in use.
Then, you can be in a position to repair/replace and other tech
tasks with your computer, and not have to re-install. Just clone
or boot from an external clone. (Disk Utility can make/move .dmg
files and disk images of your installation can be re-used.)

Good luck & happy computing! 🙂

{edited}

You don't have to register OS X and are allowed to install it on as many volumes you want as long as all of them are used with the same computer..

That's the hard way. The easy way is to use Carbon Copy Cloner or SuperDuper! to clone the internal to the ext HD. Then, if you need to update anything, just do the int and use the incremental option to update the clone. As for the TM backup, it will only recognize the volume on the internal HD. After an update installs its stuff, the package in /Library/Updates/ is blown away by the installer.

You'll have to check the Time Machine forum for info on it, since I don't use it. IMO, restoring w/TM takes longer than restoring bootable backups/clones. Additionally, it needs doing to ensure that it's viable. CCC can do file-level cloning which eliminates fragmentation, but which isn't much of an issue with Mac OS X.

Where you asked this question:

"...I've noticed when there is an update ready to be downloaded and installed it puts the install package
in /Library/Updates however after the update is complete the package is removed from this directory.
+Where does it go+ ?..."

^ Should have an answer; as I've noticed this as well. Due to some lack of ability of Software Update
to utilize a previously downloaded/saved install package later, when it may be convenient to do so; &
in my instances when dealing with this matter, have eventually had to download the file via Software
Update at least once, even after installing the full download version from Apple's web page directly...

+In one case, in particular, Software Update tried to download an existing package a second time+
+and when I quit Software Update, that tiny 1% of the download held me up for a few hours. Sure, I+
+could have 'ignored update' even while the computer was otherwise happily running the same!+

It can be a hassle. So, since I have more than one (Tiger) version running, I get the stand-alone D/L
and then recycle it between the computers needing those. And try to get the Leopard 10.5 updates as
direct downloads, too; so I can re-use them when convenient for me, offline. And burn those to DVDs.
Plus make full computer clones on boot-capable externally enclosed hard disk drives; primarily FireWire.

Anyway, for the most part your main inquiry was covered at least twice. However, where these files go
and why Software Update can't or won't use the already available(?) downloaded update package that
is somewhere in the computer (in Leopard 10.5 and in Tiger 10.4) is a mystery to me. Software Update
can make a job out of an easy method, especially if more than one system will be seeing the same and
if they aren't all linked in a networked fashion to be administered remotely and upgraded all together.

Should be about mid-summer there in Oz, huh?
We've already had weeks of sub-zero °F here.

Not so bad. Nothing like -55°F and calm, though.
Good luck & happy computing! 🙂

As I noted, in SL, the update's temporarily downloaded to /Library/Updates/, but blown away by the installer. Early on in beta-testing, I saved a copy of the downloaded package folders to another location, so as to preserve them for later installation. Became a hassle and now just manually download the updates, then run SU to further test that procedure.

Thanks for the feedback. Good computing.