I posted a thread a couple years ago about Don Carlos marrying the cousin who eventually became his father's 4th wife(oh, those Hapsburgs!) instead. but, an even But, there is something more fiendish possible.
Supposedly, Don Carlos told his confessor late in 1567 that he'd had thoughts about kiling his father, Philip II of Spain. Early the next year, Philip II came with a group in full armor to imprison Don Carlos, and he died 6 months later from pretty much self-inflicted gruesomeness.
Let's say his confessor is ill that day or he just acts before telling. What happens? Would the Spanish court have any recourse? The king has just overthrown his father and committed murder, but now he would be incredibly powerful and given his temperament... would Maximilian II, the Holy roman Emperor, actually consider sending troops to try to claim the throne of Spain for his wife, and overthrow the obviously insane Charles II?
Portugal is also interesting. They were in a position to eventually (in 1580) be ruled by Philip II, but this will bring awful terror to them if they think Don Carlos could be king. might Sebastian marry more quickly, putting aside his doubts about the light suppression of the Huguenots at the time, and marry Margaret of Valois if he realizes a Cardinal wo will not marry is the only person standing between Portugal and rule by Don Carlos?
(Then again, a couple other things could change there, too - Sebastian may choose not to go into battle or, more likely, the Pope could allow Henry out of his vow if Charles II is still king of Spain so henry can marry and continue the Aviz line.)
Given how insane this Charles II is, I could see anything up to his choosing to try to invade China or Japan. Which would have been great if Id done my "Mighty Houses Have Struck Out" timeline with this POD, but it was easier to knock the Borbons out with the Hapsburgs with an early 1600s POD and besides, there you have a lot of natural deaths. the things Don Carlos could cause were so dark, though...
then again given the taste some have for dystopias, it could make an interesting (if mostly the Chinese sense) timeline.