He's how it works in XP - not sure if it will work on Vista. I needed to change a program that is much older than UO, on a friend's Vista computer, and it won't let even administrators alter files in Program files (was needing to change the CD config for Masters of Orion II to look for a folder on the HDD instead of the CD - a one line text file, and it refused to let me change the file).
XP instructions:
1. Have both machines turned on. On each machine, go into program files, and find the EA Games Directory. In that folder, there should be a folder for Ultima Online 2D Client (or whatever your install source was).
2. Either copy the folder on the fully patched machine to the Shared Files folder on the other machine via your network, or copy it onto a USB flash drive.
3. Go to the other machine (moving the flash drive to it, if using that method). Make a backup copy of the old install, or rename it, within the folder.
4. In a new My computer instance separate from the other one, find the folder you copied from the other machine. Copy it into the EA Games folder.
5. If the new folders is the same name as the old one, you'll be prompted to replace files (which is why I suggest making a copy of the old folder as a backup). If they are different, then you'll need to rename the new folder with the old folder's name before the copy process (after backing up the old one, of course). This will keep the shortcut pats the same.
6. Make sure that the Patch folder is empty, and delete the patchlog.
7. Restart UO to make sure the copy process succeeded.
I've done this between 4 different machines over 7 years to solve patch issues, with no problems. OF course, I've only done it with 98SE, ME and XP machines, so I can't guarantee it can be done easily with Vista or W7 machines.