You will need to contact local counsel in Minnesota. I am, however, giving you this general advice that I have posted before:
International Parental Kidnapping is a federal offense located at 18 U.S.C. 1204. Custodial Interference is a crime in the State of Minnesota as well. Now, with that said:
When traveling outside the United States, you usually need a 'Hague Letter' explaining your itinerary etc..This letter is used by customs and law enforcement to allow the child to exit the country and re-enter. [ And you've know this and have tried to get the biological father's consent..] And while the father is not signing off on this letter, there are a couple of options you can look at:
First, if the father has relinquished all parental rights, than you really shouldn't have to be concerned, except that it's best to get an opinion from counsel in the state you're in to see if there are any unique Minnesota issues you need to be aware of...Second, it may just be safer to get a judge to sign off on a visit before you depart - again, check your local Minnesota laws with local counsel for this issue.
Frankly, you shouldn't have that much of a problem if you have no barriers in Minnesota and the trip is a temporary stay outside the United States with the child.
Please take this to local counsel ASAP to avoid a delay!
Sign up to receive a 3-part series of useful information and advice about child custody law.