The LayoutPanels will propogate the resize event by using the
ProvidesResize and
RequiresResize interfaces.
So as long as this chain is unbroken it should work without you having to do anything.
So if you want to place your own widget between two LayoutPanels then you have to implement both interfaces.
However your case seems to be a little bit different. I am not sure if just setting the first DockLayoutPanels width and height will cause the onResize function to be called (you can debug to check).
You should call forceLayout() on your first DockLayoutPanel after you set its dimensions. This will layout its child (including the embedded DockLayoutPanel).
You might also have to implement the ReqizesResize interface in your MyOwnScrollPanel and add it to RootLayoutPanel if you want the LayoutPanels to adjust when the browser window changes.