If I run TES5Edit through MO to clean the DLC is there an option to rename it something like Update Cleaned and select it like any other mod? There are mentions in posts about running the cleaned DLC as a mod but thats a bit vague as to exactly the steps needed to do so. I would like to keep both versions in MO and just not install the uncleaned version. I really don't understand TES5Edit I just follow the step by step instructions on YouTube and that part is not there.

Yes you can. I have mine named in a similar fashion, Dawnguard - Clean, Dragonborn - Clean, etc. I put the backups in a separate folder just because that's the way I prefer it but you can put them wherever you like. If you want to keep them in your "mod list" that's fine, just don't activate them. To be clear I didn't rename the actual .esm files, just what they're called in the MO "mods" window part of the app because it makes it easy to see at a glance what files are there and active.

Edit: If you're still new to MO Gamer Poets and Gopher on YouTube are your friends. Here's one about cleaning masters from Gamer Poets: https://www.youtube.com/watch?v=i50wxDuEnn0