Thanks for the answers guys. Emperor Constantine, if I remember correctly, the stadtholder was less powerful than the king of England at the time, perhaps having more similarities to the later British monarchs, mostly just being very wealthy people whose opinion was very respected. I might be wrong of course. As to how they might split apart, the Dutch technically elected the stadtholder, but the position was practically hereditary. Perhaps after a few generations they might elect someone else, perhaps due to neglect from the now mostly-English monarchs. The game is Victoria 2, a grand strategy game by paradox. It spans from 1836 to 1936. If you are interested in the time period (the concert of Europe, the industrial revolution, spheres of influence) I would suggest picking it up the next time it goes on sale.
Matteo, I think that the coalition is possible, but I don't think it is certain. How would they fair against the other crowned heads of Europe? It sounds like they are currently exhausting themselves in a war between the French, Bavaria, the Ottomans and everyone else(?). Perhaps this coalition might not grow very large due to this? Or perhaps it might happen later, closer to 1700. I don't know what shape England's navy was in at this point, but, if Brittania was ruling the waves as they would later do, is it possible the English might land their armies in the Netherlands and rely on their navy to prevent invasion of the island? Surely the Dutch and English navies combined could defend Great Britain's shores, and it's quite reasonable to expect a combined English-Dutch army to be able to hold the Netherlands defensively, yes? I'm very interested in your opinion on the matter.