Is there a way to hide a toolbar while in Page Sorter view? See attached.
CorelDRAW already has a Command that allows a one-click toggle of the Toolbox.
Look under Options>Workspace>Customization>Commands, and there is one named, "Toolbox". Drag that command to the toolbar or menu of your choice, or assign a keyboard shortcut for that Command, and you're there.
Have you tested this yourself Eskimo? Make your toolbox float vertically. Now use the button you speak of to hide and restore it. Tell me what happens next.