He definately stayed on as Stadholder in The Netherlands, the entire idea behind the glorious revolution and all was to prevent England from forming another alliance WITH the catholic French to start another war against the Dutch republic. Instead, the Anglo-Dutch(-Austrian-Spanish) alliance prevented France from becoming too dominant on the continent.
He stayed stadholder until he died, he kept visiting the Netherlands regularly and on several occassions for months, esp. during the militairy campaigns in spring/summer. But also to relax with his friends at Het Loo. His wife Mary stayed home in England, much to her dismay as she never wanted to leave her Dutch friends and palaces. Life in the quiet, tidy, small and calvinist The Hague suited her better than all the intregues at the British court. After Mary died the king did not visit The Netherlands very often (or at all), and stayed in London.
Originally the stadholdership was NOT hereditairy. The stadholders were the representants of the dukes of Burgundy (later the German emperor/king of Spain) in the 17 dutch provinces. At the time of the Dutch revolt against the Spanish, prince William of Orange was stadholder of Holland & Zeeland. The stadholdership became de facto hereditairy, both his sons became stadholders, and his grandson Willem II became stadholder too. However, the house of Orange usually had the powerful regents of Holland and esp. those of Amsterdam against them. So when Willem II died the position of stadholder did not go to his son (who was born after his death), but remained vacant. In the 'disaster year' 1672 the Netherlands was invaded by France, England, Colgne, Münster etc. and the mob blamed the regents. Willem III was installed as stadholder, and over the years he would get more and more powers. During this time the stadholdership became hereditairy officially, but Willem III had no children.
After his death in 1702 the regents wasted no time to claim a second stadholder-free period. Though the heir of Willem III was his Frisian cousin Johan-Willem-Friso of Nassau Dietz. JWF was however stadholder of the three northern provinces: Friesland, Groningen and Drenthe. The other provinces (Holland, Zeeland, Utrecht, Guelders) had no stadholder. When the French invaded in 1747, in what proved to be another bad war for the republic, people turned to the house of Orange again. Johan-Willem-Friso was already dead, but his son Willem IV became stadholder of one province after another. In the end he would be the first stadholder of ALL 7 provinces, and the court would move from Leeuwarden (Friesland) to The Hague. The stadholdership became hereditairy once more, and this time also in the female line. The republic was a monarchy in all but in name, though not an absolute monarchy like France. Willem IV was married to a British princess Royal btw: Anne of Hanover. In 1795 stadholder Willem V and his family had to flee from The Netherlands for French troops. He would be the last stadholder, after the congress of Vienna in 1815, his son WIllem VI would become king WIllem I.
