Update: So my wife has a different Amazon account (but still sharing Prime etc. as a family). When downloading the Alexa app to her phone, it said both Dots were registered to her account but at the same time it said on my app it was registered to my account... Tried to de-register the Dot on her app (disappeared on my app as well) and registered again. Didn't work. However, for some reason my wife's account is the dominant (lack of a better word and probably accurate) and she didn't have the right skills connected to her account. After adding Smartthings (and all my 50 smart devices, seriously, Amazon has to create a family account for Smart homes), I finally got it to work. But, I still can't figure out why only one Dot was not working, but the second was. And for all future additions I do to Smartthings, I have to update both my and my wife's Alexa app, not very intuitive.
Again, Amazon has to figure out a smarter way for cross-user implementation in a home.