As I understand it, your questions are:
Will you be able to upgrade to Mavericks without purchasing intermediate versions of OS X?
Largely, this has always been the case. Once you have 10.6 and the App Store installed, you can upgrade to the newest version of OS X that your specific Mac's hardware can handle. If you had 10.6, and didn't upgrade to 10.7, you could certainly have gone straight to 10.8 if you wished, and many people did.
Second, can you give your son your copy of 10.6? Does Apple place code on a machine preventing it from being reinstalled elsewhere?
I'm not speaking for Apple here, but I really don't think they would object in the slightest, especially since you've long since moved on to newer versions of OS X. They don't "lock" an installer to a machine in any way.
Do note, thought, that the older a computer, the less likely it is to run newer versions of the OS. Even Macs which Apple officially qualifies may not work optimally with the newest version. So do make bootable backups of your current system before you upgrade. We don't yet know what the exact supported models are for 10.9.
In regards to the Snow Leopard copy. If it came on a gray disk with your Mac, unless your Son's Mac is the same exact model, it will not work. If it is a retail copy of Snow Leopard (whiteish disk with snow leopard on it), then it should work.
If you can't make the disk work, you can purchase Snow Leopard for ~$20.00 on the Apple Store (not the Mac App Store).
The reason you have to purchase the interim OS, in this case, is you need that OS to do any upgrade to Lion, Mountain Lion, or future. Anything prior to Snow Leopard does not have the software capable of running the App Store, which is required. Apple isn't going to crack open Leopard to provide an App Store as all development on that OS has ceased.
Also note that you should keep that Snow Leopard disk around just in case you need to replace your hard drive. You can create an external Recovery disk which will alleviate the need for the disk, but I wouldn't discard it just in case.
Your answer to my question regarding 'sharing' my redundant Snow Leopard CD with my son seems at odds with the answer given by the next respondent.
They are both correct:
Once Snow Leopard has been "ugraded to Lion or Mt. Lion, its EULA specifies that it may not be used on another computer.
That being said, Apple encourages the customer base to upgrade and purchase Lion or Mt. Lion by allowing multiple copies to be used by each family member from the initial purchase. Apple also gave away free Snow Leopard discs to expiring members of MobileMe, so that they could easily "pay" to upgrade to Lion for iCloud.
This course of conduct on Apple's part would seem to indicate the temporary installation of Snow Leopard on your son's Mac to then upgrade since you have already paid for Snow Leopard and Mt. Lion is permissible.
There is no coding or serial number on Snow Leopard client install discs.
Barney's caution is correct: you must either have a retail Snow Leopard Install DVD that you originally purchased for an upgrade to Snow Leopard, or you must be using the grey Restore DVD that came with the same model Mac that your son has.