I am not sure what you mean...
I did not have calculation problems.. I see no formulas and your Pivot Table is okay...
You can hide the (blanks) row, by right-clicking there are choosing hide.
I added new Customer Part ID's and Shipped Quantities... and when I refresh the table they got added to the list....
To make the refresh on a button, remove the code you added for refreshing and instead add a new module to the editor window with code:
Then add a button to your sheet (go to View|Toolbars and select Forms to see the toolbar, select and drag the button icon onto your sheet, then assign the macro above to it....
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