Have you tried to install the UO patch before RED? That works with the full version, so I think it should work with the patch too.
1. Go to C:\User\(yourusername)\Documents\My Games\Sid Meier´s Civilization 5\cache
Delete everything inside.
2. Go to C:\Users\(yourusername)\Documents\My Games\Sid Meier's Civilization 5\MODS
Delete all monds you want not to use and all old mod versions. Trag the rest out of the folder.
3. Download the new mod´s and mod updates you want from civfanatics.com.
4. Start CIV V and go to the Mod menu.
5. Alt + Tab out of the game and place your first mod into the C:\Users\(yourusername)\Documents\My Games\Sid Meier's Civilization 5\MODS folder.
6. Alt + Tab in the game and press install mods.
7. Do point 5 to 6 until all mods are installed
8. Enjoy!
P.S.: This question comes up a lot, what about a F.A.Q. for Thal´s Balance Mods?