Hello, I am Keith, one of the experts on Just Answer and pleased to be able to help you with your question.
Sales within the EU are standard rated supplies so VAT must be charged. If your customer is VAT registered in Ireland and you have their VAT or equivalent number then the Reverse Charge may apply. In this case the book keeping transaction is as follows: you credit output VAT with the tax on the car and immediately enter it as a debit input tax item thus effectively making it zero rated. Your invoice should quote both the VAT numbers. You will be required to make periodic EU Sales Lists Returns to HMRC.
Please don't blame me I didn't invent this crazy system.
I do hope that you have found my reply of assistance.
No indeed it does not! I would be inclined to charge the tax on the margin under the conditions set out in your question.