Initially billed as a cultural trip, Usha Vance had planned to visit Nuuk and attend events, such as a popular annual dog sled race on the sparsely populated island that is home to just 56,000 people. 

That changed after her husband said Tuesday that he would join her, an announcement that was met with widespread anger in both Greenland and Denmark, which controlled the island for 300 years until it became a formal territory in 1953. Although Greenland gained home rule in 1979, Copenhagen…