After Prince Harald had discovered Atlantis, the Dutch (to be specific: The brothers Jan and Kees van Houten) were the first European nation to follow the Danes. The fact that both countries were in personal union under Gerhard II since 1417 probably helped.
In 1435 however, Black Death hit the New World, destroying the small European settlements too; other trade places had to be given up, since the Atlantean trade partners had died or didn't want to have contact with the Europeans anymore. They now concentrated on a few places: Haraldsland (Newfoundland), New Jutland (Nova Scotia), Prince-Harald-Island (Manhattan), Nieuw Zeeland (Atlantic City island), plus the Scottish-Norwegian colony on Martha's Vineyard.
Meanwhile, Denmark and the Netherlands had split again, so in 1438 their respective kings finally agreed for a compromise in the New World, negotiated by the pope: Denmark kept the northern colonies (Prince-Harald-Island, Haraldsland, New Jutland). The Netherlands got the Southern colony of Nieuw Zeeland and were allowed to colonize the lands further South.
Soon, Nieuw Amsterdam (OTL Atlantic City) saw settlers (both Dutch and Germans) come to spread slowly throughout OTL New Jersey.
After the anti-Danish War (1509-12), the colony doubled its size by getting Danish Anderland in the peace of Hamburg.
The end came with the Anti-Dutch War when France and Denmark-Braunschweig fought the Netherlands 1630-35. In 1632, Denmark-Braunschweig defeated the Dutch in Atlantis in the battle of Nieuw Brugge (OTL Easton, PA - later renamed Neubrück). In the peace of Bremen, the Dutch chose to keep their Caribbean colonies, gave Denmark-Braunschweig Nieuw-Nederland instead.
1642, the colonies of Denmark-Braunschweig (Martinsburg, Waldstätten, Nieuw-Nederland, Haraldsborg and Anderland) were united under a common administration. From then on, over the centuries Nieuw-Nederland (now more commonly called Neuneederland) lost its specific Dutch character.