It's funny because I started with the Avalon tutorial from there and replaced the contents for the window with your XAML (very similar, by the way), and the problem you are describing is not happening.
Then I realized that the tutorial uses AvalonDock 1.1.1692, and the latest version is 1.1.2691, and you describe the behavior.
Look at the source code showing the attached property specified by the ResizingPanel with the name ResizeWidth, which by default is 1 * => autosize.
If you change the first DockablePane as follows:
<ad:DockablePane ad:ResizingPanel.ResizeWidth="100" >
You will get the desired behavior.
Hard-coded widths cannot be used, so I changed it to
<ad:DockablePane ad:ResizingPanel.ResizeWidth="{Binding ElementName=dc, Path=Width}" >
after the name of the internal DockableContent dc
source share