Just a sketch
Assume Peter Stuyvesant is sent to Dutch Brazil and, more ore less, reorganise and secure the plantation colony as, masterly described in EdT's 'the bloody man'.
The following effect's on the North American and South America trade post and colonies
At New Amsterdam, after the order to resign of Director Kieft, in 1645 the council of Twelve take matters in their own hand.
After opposition against another director of the WIC, New Amsterdam will receive city right s in 1648, followed by Fort Orange, ( Albany) in 1650).
This is several years earlier than OTL.
A prominent colonist van der Donckt travels to the Dutch Republic in order the promote the colony and to persuade people to migrate. During his visit he achieve a rule of the State General, the government of the Dutch Republic, that a fund will provide the cost for transport to New Amsterdam and that ships are committed to take passengers on board. Even the whole scheme was not that successful never the less the migration to New Netherland turned in a steady influx.
The migration to New Holland, Dutch Brazil, was far less, largely due to the restriction the WIC still had on this part. The planters were bound with leg and feet to the WIC who had still the monopoly on the slave trade. A monopoly which the WIC used to monopolise most of the other trade.
The first Anglo-Dutch war was paraxial a relieve for the planters. The war disrupted trade and control of the WIC which. The planters, in search of income, found this by trading with Spain, France and Portugal. The war had minor effect on New Netherland.
After the peace treaty of 1655 the WIC tried to regain their control over their Brazilian colonies, in which it only partial succeed. Instead the city council of Maurits-stad (Recife)in 1662, sent an envoy to the Dutch Republic to grand more rights. Their complains and demands were point of long debates which in resulted in more restrictions of the WIC, city rights for Maurits-stad, Frederick- stad, Fort Keulen and the settlement around Fort Maurits.
1665 Second Anglo- Dutch war, which started with the attack on New Amsterdam. The Burghers New Amsterdam and the colonial militia defend the city against the English but surrenders in the end.
English pirate attack on Tobago is repelled thanks to the accidental arrival of five ships, among them one war ship from Maurits-stad.
Due to uncertain trade lanes, planters in New Holland contract Spanish, Portuguese and French slave traders and transports to ship their products to Europe, effectively breaking the WIC.
1667 End of 2nd Anglo-Dutch war, New Netherlands is returned to the Dutch Republic. New Holland is enlarged with former English plantations along the river Suriname.
1672 Dutch war and 3rd Anglo Dutch war. Trade with Europe comes to a halt.
Tobago attacked by 6 English ships and 600 soldiers, but attack repelled by the colonist.
North and South American colonies grew considerable and gain more self-control. New Netherland is granted representation in the Estate General, making it de-facto a Province. A fund is created which finance a squadron of war ships to secure the trade lanes an protect the colonies against raiders.
1677 Heavy French attack on Tobago which is repelled. Later that year the French attack again with a large force but after 4 days the French are destroyed and only due to the timely arrival of the South American squadron.
1681 Since the ‘dragonades’ in France a ever increasing number of Huguenots from France entered the American settlements. Especially the Dutch rulers in the South American colonies of New Holland, saw opportunity to enlarge the protestant population. They tried to persuade the refugees with attractive shipping rates and success stories. After the revocation of the Edict of Nantes in 1685 the migration toward both New Holland as New Netherland grew considerably and the years 1685-1690 saw the largest influx of settlers in New Holland ever.
1702 Just before the War of the Spanish succession New Amsterdam was a city of significant size with around 6000 people with almost the same number in the other parts of the colony. Maurits-stad had around 8000 free Burghers with nearly the double in the other parts of New Holland. Tobago 4000 free Burghers. The colonies of Berbice, Suriname and Essequibo were more plantation colonies with a relative small European population.
Despite economic losses most colonies were spared from attack or raids.
During the 18th century the population of European descent grew considerable as with the self-consciousness of the Free Burghers. New Amsterdam turned in a real copy of its large counterpart in Europe, growing wealthy as trade port of local products, slaves and colonial products form the Southern colonies also the British colonies.
Maurits-stad transformed in the largest city of the South American East coast, and showed their wealth made with export of colonial products with rich houses and buildings among long lanes. The City also included the largest university of the new world.
1776 New Amsterdam is confronted with the American revolution and due to it support to the rebels, it sells all kind of supplies, is occupied by the British. After the American independence it remain under Dutch control how ever it was one of the first to make trade and custom agreements with the new nation.
When the Dutch Republic become a puppet of revolutionary France it asked to join the United States of America.
The more aristocratic Burgers and plantation owners of the South American colonies were enthusiast followers of the en-lightment but were suspicious of the revolution as it enfolded in France and the support it had in the Dutch Republic.
New Holland how ever remain loyal but when the Batavian republic is terminated in declares independence , which is for a large part motivated by economic factors. In 1803 it took control of the various African trade stations among the Gold coast, the Congo river and the Cape colony. It allied them self with Great Britain out of self-conservation and trade opportunities.
After the fall of Napoleon and the declaration of the Kingdom of the Netherlands, New Holland submitted itself to the new monarch nevertheless with such amount of concessions that it was nearly independent.