DaVinci Resolve: hide timeline viewer
The current way to accomplish this is to either:

1) Toggle the menu [Workspace] > [Single Viewer Mode] 

- or - 

2) Toggle the [ ] / [][] button (top right of the viewer)



NOTE: Resolve will only enable the options and allow the use of two viewers if it has enough screen space (screen real estate) to do so. And that is probably the reason why opening/closing the Inspector affected the dual view.

(Resolve 15)