You could add a metadata column to the folder and documents within it and then create a view with a filter on the new metadata. This will also help people see the power of metadata and views and help ween them off their reliance on folders.
Edit: Example - here is an example of how to do it. Note, this is a basic outline and there are variations on other settings you can choose which I will not mention here.
Go to your document library settings and add a new column, make it of type "single line of text". For this example, I've called it FilterBy. Now, whilst still in the doc library settings, click on "Column default value settings" under General Settings.
On the left you will see the list of folders in your library. Click on the one you with to filter on and then click on the column header to edit it. Enter a default value for this column.
A green cog should appear on the folder to show it has a default value applied. Now whenever you create or upload a document to the folder, it will have the default value applied to it.
Now you need to go and create a view. Set a filter on the view on your new column and default value. Now the magic bit, Expand the Folders option and check "Show all items without folders" and then save you view.
When you now select your view in the doc library, only the docs in that folder will be visible. If you set the view to the default view in your web part, that should hopefully give what you are after.