You actually can do this because you have valid Windows licenses for both PCs. Even though your new laptop came with Vista pre-installed, Microsoft does allow you to "downgrade" from a more recent version of Windows to an older version of Windows... so your Vista license legally allows you to install XP on your laptop if you should choose to do so.
Now there is nothing "mean or petty" about any of this. All Operating Systems, including the Mac OS, are sold as one license, one computer. Fortunately, you have a license for your laptop, so you're OK in that respect.
For your second issue, where you put the disk in and the install selection is greyed out... well, that's because Windows does not allow you to downgrade a newer version of Windows with an older version on the fly. If you really want to downgrade your laptop to Windows XP you have to do so by booting from the installation CD and reformatting your hard drive. You'll then be allowed to install your copy of Windows XP on a clean system. Do be aware that this means that you will lose any applications, music, photos and files you may have on the laptop. Backup your personal files first and make sure you have the installation materials for any applications you may wish to replace. Place the Windows XP installation disk in your computer and boot from that disk (instead of the hard drive). Follow the on-screen procedures to install a clean copy of XP.
One last issue... BEFORE you start the process to install Windows XP, go to the website for the manufacturer of your laptop. Check to make sure they have drivers available for Windows XP for all the hardware in your system. It hardly makes sense to change from Vista to XP only to find that there is no hardware support drivers available for XP. If you find they have XP drivers available, download them NOW and drop them on to a flash drive. You'll need them to get your hardware working once you finish installing Windows XP... especially the driver for the laptop's network card.
Good luck with your downgrade!