What do I call this and where do I get one? One button z-wave controller?

Could be a switch, could be a button controller, they can both do this.

Since the title of this thread is “one button controller”, There is a list of the buttons and remotes that work with smartthings, that would probably be helpful to people specifically looking for buttons. This includes both handheld and wallmount devices. ( this is a clickable link)

However, from the content of your post, I think you’re actually just looking for a wall switch to act as the auxiliary in a virtual three-way. So I’m going to put the answer to that in the next post. :sunglasses: