Just about everything in your question is wrong.
The 1500 to 1700 is a long period with a lot of different things going on. During the entire 16th century and part of the 17th century, the hegemonic power was the Hispanic Monarchy, more commonly known as Spain, having a massive empire in the Americas.
Columbus gets to America in 1492, then goes back there in 1493, then again in 1498, and lastly in 1502. He was not only one, many more people explored the continent, like Vicente Yáñez Pinzón, Diego de Lepe, Antón de Alaminos, Alonso de Ojeda, Amerigo Vespucci, Juan Díaz de Solís, and a whole lot more. By the year 1560, the Spanish power in the Americas was quite solidly established: viceroyalties, Royal Audiences of Justice, Captaincies General, Royal Mint in Mexico and Lima, universities in Mexico, Lima, Santo Domingo, and one in Bolivia, the whole lot of elements of power.
The Portuguese were also getting their hands into an empire, setting up colonies or outposts in Brazil, Angola, Guinea, India, and creating an adequate route to the latter place. In 1580, with a lack of heir to the Portuguese throne, the closest relative with a claim to the throne was Ranuccio Farnese, son of Alessandro Farnese. Ranuccio renounced his claim in favour of his grand-uncle Philip II of Spain, who would rule over the Spanish and Portuguese empires in what is called a personal union. This union, the hight of Spanish kings' might, lasted until 1640, when the Braganças rebelled and secured the throne of Portugal for themselves.
By the mid 17th century another power player emerged under the direction of competent administrators, wise ministers, and ambitious kings: France. This country can be considered the hegemonic power for the second half of the 17th century and a good portion of the 18th century.
The Dutch would come into prominence in the realm of commerce, shipbuilding, and global power in the 17th century too, more specifically with the creation of the Verenigde Oostindische Compagnie, a private-public partnership company that would have control over the Dutch possessions, like Suriname or Indonesia. This company was monstruously powerful, even having an army, a navy, and the authority to mint coins.
The Dutch, however, did not have anything close to a monopoly on trade. The Hispanic Monarchy had set up in the early 16th century what we call "the fleet system", which was an annual convoy going from Veracruz to Seville via Havana carrying the tributes, coins, and merchandise from the Indies. Another convoy would depart from Seville towards Cartagena de Indias with manufactured goods, luxury exports, and some other supplies from the metropoli to the viceroyalties. This system lasted for 250 years, and was a total success, only twice losing a complete fleet, and losing only a total 3% of the ships that came from America to Seville. The fleet system was scrapped in the 18th century, withthe advent of liberalism, with king Charles III ending the monopoly of commerce with America through the Casa de Contratación de las Indias, and instead liberalising it, allowing many companies to trade, like the Compañía de Guipúzcoa.
America, the continent, was mostly Spanish until the early 19th century and the wars of independence. The British only controlled a relatively small fraction of the American continent prior to 1700, and definitely not the richest part. It did not have the vast mines of Potosí, Zacatecas, or Huancavelica, or anything remotely close. The part of America controlled by the British was a part too far away from the Spanish centers of power. Spain did never venture that far north, as it would have been a logistic nightmare for the viceroyal authorities.
If Britain is remembered as the "powerhouse" country of that period is because of the Anglo-American political hegemony in the 19th and 20th century, and especially the cultural hegemony in the 20th century. Spain and Portugal faded into cultural (or rather popular-cultural) obscurity, and France is not the cultural powerhouse it once was, it does not dominate the historical narrative anymore.