Dear Agerolimatos,
Sorry to hear that you are running into issues with the shipping costs not refreshing when you switch countries. Do you use the default VirtueMart checkout process (One-page checkout enabled or mult-page?) or do you have a third-party CHeckout plugin installed (Rupostel One-Page Checkout, VP OPC, CMSmart OPC, etc.)?
If you could give me access to your site, that would probably make it much easier tracking down the issue. Our contact email is: office@open-tools.net
Best regards,
Reinhold