With a direct download from Origin, Awakening may not show up as you might expect, even though it IS installed.
One thing you can do is start Origin, hover over Dragon Age: Origins and click on the information link. On the info page, it should list Awakening under the main game. If you hover over it and it's installed (and Origin sees it) it will show a Play option over Awakening itself. Otherwise, it will show an Install option. If that's the case, click on it and it will download and install Awakening properly.
Quick way to check if the UE has installed everything properly is to start up the game, then at the main screen, click on Other Campaigns. With the Ultimate Edition properly installed, it should list Five:
Witch Hunt
Dragon Age: Awakening
The Darkspawn Chronicles
Leliana's Song
The Golems of Amgarrak
If they are not all showing, then for some reason the installer hiccupped and missed something.
Check your game install directory and/or your addins folder in your Documents\Bioware\Dragon Age directory for a directory named dao_prc_ep_1. If it is there and contains files, then the installer put it there, but may have somehow glitched when it updated the addins.xml file in your settings directory.
If the folder is there, but you check addins.xml and Awakening is missing and you're feeling brave, you could try manually updating the file following the instructions here:
http://forums.steampowered.com/forums/showthread.php?t=1677021&highlight=Awakening
If it's still missing, post again and let me know if the files are even there, etc, and maybe I can give you a few more suggestions.
Good luck!
