How did you manage to live in Denmark with the Rasmussen-peddled residency laws? Older than 28?
More seriously, doesn't the US issue multiple-entry non-immigrant spousal visas? (K-visas???

) Or maybe a spouse of a US citizen is required to file an immigration petition regardless of intent to immigrate or not in order to get the spousal visa?
The LIFE Act -- listed as the third link below -- has some info that may be useful for certain non-immigrant spouses of US citizens.
http://travel.state.gov/visa/immigra...s_1315.html#3a
http://uscis.gov/graphics/howdoi/hdiknonimm.htm
http://uscis.gov/graphics/services/residency/LIFE.htm
http://uscis.gov/graphics/publicaffa...life081401.htm
It seems easier to just come in under the VWP since they are not immigrating. I don't even know if the K3/K4 is required anyway -- especially when it seems in the press release that it is not required -- and it may not be wanted because it could be conditioned on filing a petition for immigrant status.
I suggest asking a US immigration attorney in any event.