How to auto-hide tool window between two other tool windows.

I have a layout consisting of two vertical tool windows, one on either side of my application. The space in the middle is where I put my tabs using tabbed MDI. I also have a tool window docked at the bottom of this tab area, in between the other two tool windows (the equivalent of dragging it to the down arrow right below the little tabbed icon in the tool window docking UI that shows up when you start dragging a tool window).

This is all working great. However, when I tell the tool window located in the lower-middle portion of the screen to auto-hide it changes it's width to be that of the whole form and then collapses, rather than just collapsing into a tab that resides between the two vertical tool wndows (as I would expect, given it's dock position between the two verticals and not below the two verticals spanning the whole form).

Which brings me to my question: Is there a good way to force the tool window in the middle to only auto-hide to a tab that resides between the vertical tabs when it is docked between them?

Thanks,

George