Get a faster hard drive for your laptop.
Seriously now, that's probably a cache issue related to retrieving the icons on the sub-dock. Here is what I think is happening:
Docks that are currently open, and the Shelf, cache icons in memory. This is why it takes longer to open a Shelf tab the first time you access it, as all those icons need to be retrieved from disk. The slower your hard drive and the more items you have on that tab, the longer it takes.
The Shelf has an added mechanism to deal with this: after x milliseconds (i.e.; if it takes too long to open that tab), it will start displaying a generic icon for all the items that it hasn't been able to retrieve the correct icon for yet. Then, in the background, it will replace those generic icons with the proper icons as fast as it retrieves them.
Once all icons have been retrieved for a tab, they are cached in memory. The second time you access that tab, the Shelf no longer needs to retrieve them from disk and the tab opens an order of magnitude faster.
As a side note, changing the icon size of the Shelf and certain system events flush the internal icon cache.
Now, docks also cache icons in memory, but because they are always open they do not have that temporary 'generic icon' mechanism to smooth things out if it takes it too long to retrieve all the icons.
When a dock is closed, its icon cache is discarded. Not a problem with the 'parent' docks because they are usually never closed (even when hidden beyond the screen edge).
Sub-docks, on the other hand, get destroyed when you close them (and there goes their internal icon cache when that happens).
Now, Windows itself also has a file cache. When you open a sub-dock, Windows caches the files the sub-dock accessed in order to retrieve the icons. Even though the sub-dock's icon cache is destroyed when you close it, the Windows file cache still holds those files in memory, and will for a time.
But, as you work on your system, the contents of that file cache are gradually replaced with other stuff. So, after a while, all the icons will need to be retrieved from disk again when you open a sub-dock.
Of course, it never occurred to me people might run into this issue with sub-docks.
To solve this I will need to apply the same technique used for the Shelf: if it's taking too long to render all the icons in a dock or sub-dock, render a generic icon instead and then later replace it with a proper icon. This way the sub-dock will open nearly instantly and users will be able to work on it even if it's still busy retrieving the actual icons from disk.
You will have to wait for the next release, though.