The only way you would have paid VAT twice is if you bought from a UK shop too silly to export properly, or else they did export properly and ripped you off. Barefaced are well versed in exporting with no sales tax incurred until the destination country's customs clearance. Then that is between the importer and their govt.
If it's anything like NZ and UK you would have been charged Eire VAT on the export price and cost of shipping. On top of that, whatever clearance fee applied with your shipper. Maybe VAT on that fee as well?