So I know this glitch is related to having Dawnguard installed but is there anyway to do this without uninstalling and reinstalling Dawnguard?

I bought the Alchemy Lab on my new character (Orcish Warrior) but it doesn't show up.

Some of the Properties being passed into the lab enabling script got glitched, set to no value, there are some fixes for this on Skyrim Nexus and Steam Workshop.
These not being set is why you can keep flusing your money down that option too.

Steam Workshop was intended to empower theconsole with these mods, and others.
Good luck.

http://steamcommunity.com/sharedfiles/filedetails/?id=88446940&searchtext=dawnguard+breezehome+fix