If I understand your requirement correctly:
when shipping from warehouse in Europe A, you want to charge VAT of country Europe A.
When shipping from warehouse in Europe B, you want to charge VAT of country Europe B ?
If that's the case, did you look into setting each warehouse/Site with a different VAT group?
Each VAT group contains the tax code of the country of the warehouse.
This should default into the sales order lines, and give you a correct calculation