divorce with an International marriage license

Why don´t you ask the Danish Embassy instead - they are the ones to know.

Once you got been married you reciecved an international marriage certificate in five languages.
Did you get your marriage certificate legalized? If not see below:
http://www.um.dk/en/menu/ConsularServices/Legalisation/TheApostille/

Well, it took a week to go through the whole paperwork thing, so I am pretty sure it got legalized. It was back in 2004.

What is legalisation?
Legalisation is a confirmation that the signature on a document is genuine. The actual legalisation process consists of a stamp (Apostille) and a signature. Legalisation does not have anything to do with the contents of a document.
If you do´nt have the Apostille you can get one now -see below. Address, price everything

http://www.um.dk/en/menu/ConsularServices/Legalisation/Legalisation.htm

Well I left my base on a monday, did the paperwork on a tuesday and then had to wait till a friday to get married because they had to process the paperwork... pretty sure that during that time they had the paperwork legalized (it's got stamps and signatures on it).

Original signature
The document must bear an original signature of the authority that has issued it in order that it can be legalised. If the signature can be accepted, the document is legalised by means of a stamp and a signature.

You better contact the Embassy. I cannot understand how a marriage certificate can be issued before you get married. Before you get married the most you can get is an allowance to marry. Which means all the paperwork to prove you are you and you are not married already and all that kind of things.
After the marriage cermony you get a marriage license.

What base?

Are you US military or a foreign military?

Do you think that such makes a difference in Danish law?

Veteran of US military

I contacted the Embassy from your orignal link and they sent me back my answer (that I can get divorced in the States, so long as the court aknowledges that the marriage certificate is legalized). I was issued the marriage certificate after the wedding ceremony, not before.