The thing is this is a partisan split in Britain. The Whigs genuinely preferred a Habsburg Spain and Austria than allowing the French to get back in the game.
Back in the game: France was THE game. Top dog. Everyone had to join together to knock down France. Spain was the one looking to get back in the game after decades of incompetence/decline.
Habsburg Spain and Austria (not in union) was status quo. Austria wanted the whole pie. England wanted the Spanish empire broken up, and as long as France stayed out of the Netherlands, was open to various ways to split it up. They preferred France in Italy. Louis practically forced England into war by attempting to grab all and denying English economic interests. Without Louis being so hamfisted bellicose, the Whigs would have had a hard time mustering the support for war. Once the war is underway, and at the POD point, it was the Whigs turn to be hamfisted bellicose and go for it all.
You have to butterfly Joseph's death in 1711, or the whole thing starts up all over again. No one, including the Whigs, is going to allow a union of Austria/Spain.
for the sake of argument, assume the Whigs get their way, and France is humbled. Philip is ousted in Spain. England still doesn't want the Spanish empire left intact. Look for Savoy to make big gains in Italy, though it is doubtful Austria is going to give up Milan.
France is now free, once they recover, to attempt to take Spanish colonial possessions in future conflicts. France, as a humbled power, is going to cozy up to Britain, and Britain will likely cozy up to France as a balance of power. Will Charles unify/centralize Spain, or just muddle along as he did in Austria? Will there be anything resembling Bourbon reforms? Does Joseph (presuming he lives) strengthen Austria with his reforms? Elizabeth Farnese becomes just a footnote in history.