FYI King William's War (AKA War of the League of Augsburg) was the previous war (1688-1697). Knig William's War and Queen Anne's War were the names given to the wars by the English colonists in the Americas; AFAIK they were not so named in Europe.
A son to William and Mary (Wiliam IV seems a likely name for him) is probably going to have a firmer grip on the reins than the alcoholic and hedonistic Anne. Churchill, although he may not initially be entrusted with the command, will probably inherit it, especially if he is successful, and keep it, assuming that the level of influence exerted on William is less than that on Anne. And even if William IV does not become Staadholder he will exert great influence over his Dutch allies, so they will stay the course as well.
This will mean that the outcome will probably be less favorable to Louis XIV than IOTL; how much less favorable is open to question.