What if disillusioned French fur trappers Radisson & Grossiliers went to New Amsterdam instead of Boston after running afoul of the Governor of New France?
Say the result is a successful expedition by 1662.
During the Anglo-Dutch war the English seize New Netherlands but not the more remote, newer colony. Before the next Anglo-Dutch war rolls around, the Dutch start to realize fur profits and invest more in the enterprise. If the English are not committed enough to seize or hold the bay in the third Anglo-Dutch war of the 1670s, what would the subsequent history of the Dutch Hudson's Bay look like through the 18th and 19th centuries?