Hi Clay,
Was the amount that they gave you documented as a "quote" or an estimate"? And was there any express statement or notation on the written quote stating that it was "not a binding offer" or words to that effect?
An estimate is generally not legally binding. However, a quote is usually legally binding on both parties if it forms part of a contract. Depending on the circumstances a "quote" may be construed as an offer by one party which if accepted by the other would give rise to a contract between them. If you can show that the written quote you received was an offer and that a contract was entered into, then you will only be required by law to pay the quoted price which was agreed to, provided there were no other special circumstances written into the quote or you agreed to vary the quote.
I would firstly check the terms and conditions of anything that you agreed to or received from them to make sure there is nothing stating that they can charge whatever they want notwithstanding the quote. If there is nothing like that tell them you will be paying the agreed price end of story, because their quote constituted an offer which you accepted and that as soon as they knew it was going to be twice the amount of their quote they should have contacted you to see whether you wanted to go ahead with it or not.
Just another thought, are the additional charges DHL charges? Or could they be other import duties or taxes which DHL has no control over? In the latter case you may be required to pay them because they may fall outside the scope of the initial quote.