OK, I figured it out. Here is how you do it.
Get the printer running on your Vista 64 machine. Vista has a ton of drivers, and for the most part, it should detect your printer and start working. If not, you'll have to install the drivers from the manufacturers disc or driver download.
To be able to share the printer on the network so that it works with x86 computers, you have to install the the proper x86 drivers. These drivers are the same drivers that work with Vista 32 bit. Don't assume that drivers built for XP 32 bit will be correct just because the other x86 computers on the network are running XP.
To install the x86 drivers go the the start menu and type "printers" and press enter. You should see an icon of your printer. Right click on your printer and chose "Properties". Inside, go to the "Sharing" tab. Click the "Change sharing options" button. Next click the "Additional Drivers" button at the bottom. Check the checkbox in the processor column with the "x86" next to it, and click OK. This will prompt you to install the x86 driver. It wants you to navigate to the driver's .inf file.
At this point, we don't have the driver and its .inf file. To get the proper driver we first need to do some stuff. If your printer installed on its own using the provided drivers found in Vista 64, there should be a corresponding driver with the same inf file name in Vista 32. To get the drivers, you either need a PC running Vista 32, or the disc itself.
I had the disc, and the method I used to get the drivers from the disc was this. I downloaded Microsoft Virtual PC 2007, which is a free download. Install the program and created a new virtual PC. I then installed Vista 32 bit on it. Once there, I went to C:\Windows\System32\DriverStore\FileRepository\ and copied all of the files from there and pasted them into a shared network directory on my Vista 64 bit machine. Once I had the files, I could then complete the process of installing the x86 driver on the printer.
Its just a matter of finding the correct .inf file in the copied files. For me installing a HP PSC 750xi, the correct file was in a folder that started with "prnhp001.inf_".
When installing my Epson printer, I was able to do it another way. I downloaded the Vista 32 bit drivers from their website. Then started the installation executable. After the program has extracted all its files, I tracked down where the files had been extracted to and found the driver's .inf file there. Then I attempted to install the x86 driver. However the printer's name was slightly different in the .inf file and would not install. Pay attention to the error Windows gives you. It should the printer by name it is trying to install for. Write down that name and go into the .inf file and edit the printer name to match what Windows is looking for. After editing the file, try again. Windows should now be able to find the drivers and install.
If at any time during the install Windows should complain about the drivers not being signed or some other similar warning, most likely the drivers aren't going to work.
After you finally track down the correct drivers and install them into the printer, you should now be able to navigate to the Vista 64 machine on the network and see the printer icon. Click on it to install the printer on the 32 bit machines and test. If everything went as planned, you should be able to printer just fine.
If for some reason, after installing the drivers, they do not work, you may need to investigate further and install the correct drivers. But first you need to uninstall the incorrect x86 drivers. To do so, go to the start menu and type in "printers" and press enter. Inside the printers window, right click on the open space, not a printer icon, and choose "Run As Administrator > Server Properties". Then go to the drivers tab and find the driver you just installed and click the remove button.
I hope this helps anyone needing to run both x64 and x86 PCs on their network that need to share the same printer. I never tried running it the opposite way though, where the printer is on the 32 bit machine. That may bring with it another whole issue of problems.