A) Is this a credit card or debit card? If it's a debit card are you sure it's a second charge and not just the initial auth (which didn't disappear for some reason) plus the actual charge?
B) Disputing a charge as invalid (duplicate, in this case) doesn't require re-issue of a card. Disputing a charge as fraudulent (I didn't make this) might. Don't dispute it as fraudulent - dispute it as a duplicate. Should be easy for the bank to see if the amounts match. If not, they'll investigate.