An Orange Dynasty

Following in the wake of the so-called 'Glorious Revolution' in England and Scotland that toppled King James II/VII, the parliaments of both nations passed acts that solidified the rule of his usurpers; Stadtholder William III of Orange and his wife (the daughter of James II/VII) Mary II Stuart. Together, the two co-monarchs loosened the powers of the British crown by abiding by the recently established Bill of Rights, furthering the powers that their subjects could wield whilst simultaneously looking abroad to distant lands in hopes of promoting the commercial, military, and colonial capabilities of the English, Scottish, and Dutch nations, and ultimately through conflict and mercantile ventures abroad, the governments of the co-regent-led personal union dragged their countries into the 18th century and the dawn of enlightenment.

However, what could have been for the couple and their vast empire was ultimately stifled by their inability to produce an heir, Mary remaining childless whilst William was often abroad fighting against Jacobites and French on continental Europe and Ireland, and after her untimely death of smallpox in 1694 at the age of only 32, all hopes for an English dynasty for William's House Orange-Nassau dissipated, the line ending with the King's death of pneumonia aged only 52, the crown being handed over to Mary's sister Anne.

This timeline shall detail a world in which the House Orange-Nassau of England didn't die out with the death of William III and his able wife, but continued on with the birth of two sons into the tulmoteuous years of the 1700's; the birth of modernity, and the age of enlightenment. What effect would An Orange Dynasty have upon the world?