Charged twice for one online order, what do I do first?

Wait for both to post. A pending authorisation and the real charge often look identical for a few days, and the hold drops off on its own, usually within 3 to 5 business days, sometimes a week. If both show as posted and you only have one order confirmation, email the store with the order number and both transaction dates and ask for a refund of the duplicate. Keep that email. The bank dispute is for when the store ignores you or refuses, and the bank will ask whether you contacted the merchant first, so do it in that order.