So, I try to shoo it off, dismiss it, tell it to wait, but nothing worked. Not only that, but whenever I interacted with it, my actual follower would dismiss. Whether it was a mod issue, or just a bugged dog, I don't know, but I do know that I haven't interacted with this dog previously on this character.
Now, it's nice to have a dog around, but definitely not in falmer infested dwemer ruins, and definitely not if it causes glitches with my actual follower. So, no other option, I crossbowed it...three times. The really unpleasant part was that it just sat there with a dopey look on its' face.
Sometimes this game svcks.