Don Carlos is less unstable and lives londer, inheriting Portugal, then the rest of Spain. This Iberian Union is more integrated and maybe there can be less restrictions on colonial settlement eventually. With Portugal and Spain united, you just have to get the British, French, Dutch, Nordics, and Russia out. By the time anyone with the interest and means to go colonising gets to it, the Americas should all be at least lightly claimed and settled by Spain (maybe they can recruit settlers from other Habsburg realms as well if they need it), even if its just a nominal claim, with possibly a bunch of allied native tribes in the area.
England: Maybe Mary I can have a son with Philip II, so ou get a Habsburg branch in Britain. This branch is uninterested on stepping on their cousin's toes in the new world. Maybe they can get an arrangement where English settlers are allowed to settle some parts of the Spanish Americas, but they never establish any formal colonies in the Americas, perhaps focusing more on expanding continental holdings in France. They can inherit Scotland at some point as well, so no Scottish attempts either.
France: Change the situation at home so that French kings are unwilling to spend money on colonisation. Maybe being encircled by Habsburgs makes them pour more money into continental wars, or fortifications in the Metropole. Could get embroiled in further conflict with Britain if the British Habsburgs are pushing claims in northern France. Maybe a few particularly pious kings decide to pour some money into a new Crusade or some missionary efforts in Africa or India or something. Maybe France can get lucky in India and be more occupied there.
Dutch: With the English firmly Catholic and Habsburg, the Dutch Revolt either fails or succeeds but goes much more poorly for the Dutch. Spain could hold onto more or all of the Spanish Netherlands, maybe some alt. events in the Revolt could result in the Seven Provinces fracturing and going their own ways, maybe some combination of the two. Maybe the Dutch Revolt still goes as OTL for some reason, but the Dutch have earlier and/or greater success in the East Indies, which siphons attention away from the Americas.
Nordics: Sweden can get into trouble with Russia and Denmark. They get effectively locked in the Baltic as a result. Norway is part of Denmark. Denmark either doesn't care to go to the Americas, or doesn't care to anatgonise half of Europe (Habsburgs in Britain, Spain, and HRE). Maybe it gets embroiled in conflict with Sweden that takes all its attention.
Russia: Delayed expansion to the Pacific coast, or whoever is in charge just decides Russia has enough land in Siberia without antagonising the aforementioned half of Europe. Could get into worse conflict with Sweden, PLC, and/or China too to suck up all its money.