| When I hover over the new tabbed dock, the whole dock pops up |
Uh, it sounds like the dock is functioining like a drawer to me.
Does the dock hide until you mouse-over? If so, that is the correct functioning of the dock.
If you are looking for one tab to open, you will need to create a single tab dock - the tabbed docks operate as a whole whether there are multiple tabs, or a single tab. The displayed dock is based on which tab has been selected.
You could do something like the following:
1 - Create 3 single tabbed docks of the same size, with the tabs of each aligned as follows: 1-Top\Right, 1-Top\Center, 1-Top\Left (Note - tab alignment is accessed in Dock Settings > Size & Appearance section in the lower half of the dialog).
2 - Use the Dock Settings > Positioning section of each dock to set it as a drawer at bottom
This will in effect, create a three tabbed dock that allows each tab to be called and displayed independently of the others. You can use different sized docks as well, which you can then manually place where you want before selecting the "Show dock as a drawer" option if this suits your purposes better.
Unfortunately, there is the limitation of only three tab positions per side (Right, Center, Left for a dock located Top or Bottom, and Top, Center, Bottom for a dock located Right or Left).
If on the other hand, you do not want the dock to open until you click on a tab, you would deselect the "Mouseover activation" option under the drawer settings.
Two other items of note:
1 - You can select "Lock Icon Dragging", and "Lock Dock Position" using the Right-click tab > View menu.
2 - You can drag tabbed docks to different sizes vertically and horizontally, allowing you to create a vertical dock one icon wide. This can ony be done with the "Lock Dock Position" deselected.
I hope this helps in some way. 
