I saw this touched on in the 'Failed Marriages and Pregnancies' thread, but it wasn't explored in as much depth as I'd like, so I figured I'd pose the question directly.
What If Mary I had Philip II's son?
During Phillip II's reign, Spain reached the zenith of its power across the globe, which also means it began to decline. Revolt in the Netherlands, the failure of the Spanish Armada, multiple debt defaults, and the ascendency of the House of Bourbon reigned in what had been Europe's superpower. England had a direct role in half of these, and indirectly in all; war with Elizabeth's England sapped the treasury, Elizabeth didn't lend support to the Catholic League in the French Wars of Religion, and England aided the Dutch rebels against the Spanish.
So what if England's king and his regent were die hard Catholic Habsburgs? In terms of Continental politics, could the Dutch Revolt have been stamped out? Could Spain and England keep the French politiques from gaining primacy, and if they did, would the French still be able or willing to stop Ferdinand II, with Tilly and Wallenstein, from stamping out the rebellious princes of the Holy Roman Empire, and the Reformation with it, and thus consolidating a national state?
English affairs are wholly outside my wheelhouse, so what effect would a reigning Spanish Habsburg have on English development, specifically regarding protestantism and parliamentarianism? Furthermore, English colonization of the Americas followed a very different pattern from the Iberians, who ruled over and mixed with the natives, rather than driving them off outright.
The Early Modern period was one of the most influential in shaping the world we live in, so a small change, like a particular woman becoming pregnant or not, is going to have serious ripples.
One of may favorite PODs
! To begin with I agree that there's little chance of Mary naming her son John. Chances are the Prince of Wales would be named Henry, after her father and grandfather, or Edward after her brother and Yorkist ancestors. Probably the former as Mary highly respected her father (despite his actions towards her) and its a name that would be recognizable in Spain as well as Enrique.
Second, Queen Mary died of uterine cancer, which she had suffered from for several years (maybe as much as five, being sick at her accession). To have a son she'd have to never develop uterine cancer, which would mean that she'd live longer. How long is debatable. Her mother and grandmother died in their 50s, her maternal grand father in his 60s and her aunt Juana at 75. So at the very least she'd probably live into her 50s, meaning her reign would be extended by at least 8/9 years. So at the youngest Henry IX would be 11 to 13. Technically at 13 a boy does not need a regent, being the nominal age of majority.
Third, with a longer reign Mary would have a better lot in historiography. As one author put it "Although Mary's rule was ultimately ineffectual and unpopular, the policies of fiscal reform, naval expansion, and colonial exploration that were later lauded as Elizabethan accomplishments were started in Mary's reign.
https://en.wikipedia.org/wiki/Mary_I_of_England#cite_note-162" A longer reign means that the policies Mary began have the chance to take root, boosting her popularity.
Fourth, while Felipe II was indeed named Regent for any underage child, by the point Mary would have died he'd be King of the Spanish Monarchy, meaning he wouldn't be in a position to stay permanently in England for an extended period. On the other hand, with his wife having an extended reign and a son chances are Felipe would be making frequent visits to England, meaning that he'd probably have better relations with at least some of the English Nobility, enough to build up at least a small power-base that could act as his deputies in London. They could act as members of a Regency council or as a Privy council to advise Henry IX.
Fifth is a problem: Elizabeth. At best she'd be a rallying point for the discontented Protestants and those who hate the idea of a half-Spaniard on their throne. At worst she actively plots to depose her nephew and seize the throne. However, in my opinion Mary with a son would no doubt be more forceful in her dealings with her half-sister. Elizabeth would be married off to a foreigner to permanently remove her from England. I know that the major suggested match was with Duke Emanuele Filiberto of Savoy, so that could be the best bet.
Sixth, the Dutch revolt. Chances are it would be stillborn or die soon after it began. England is sure as hell not gonna support the revolt, considering that the Marian marriage contract gave the low countries to any son of Mary and Felipe. Although I wonder if we'd potentially see the Netherlands transferred to England early, before the crisis between Felipe and his Dutch nobles reached the point of rebellion?
Seventh, is France. After the death of Henri II of France in a jousting accident in 1558 French presence in foreign affairs basically collapsed and wasn't recovered for nearly 40 years. However, Henri II's death was basically a freak accident, one that could be butterflied away with a POD in 1555. But either way chances are that France will be focusing on domestic policies for at least the next decade, if not longer. Also, if Henri II lives another 10 to 20 years I doubt we'd see the French wars of Religion be as numerous or as destructive. Henri II would be more likely to keep up the war against the Huguenots until they are permanently crushed.
Eighth, the Parliament of England. Under the Tudor dynasty Parliament was a rubber stamp assembly, which it would no doubt remain with a native monarch at the helm. Parliament basically saw in opportunity with the accession of James I to gain the power they thought they deserved. Here, with the King a member of an international dynasty ruling much of Europe, that chance to challenge the Sovereign isn't there. The power of the purse-strings mean little when your father can send fleet loads of gold and silver your way.
Finally, as to Scotland, the thirty years war and the HRE, that's hard to guess. Scotland's Presbyterians only won against Mary of Guise thanks to support from Elizabeth I. No English support means no Protestant Scotland. But, with the Queen of Scots in France married to the Dauphin, there's a lot of opportunity for a Scottish Huguenot style group to develop, becoming a state within a state, like at La Rochelle. The HRE is harder to tell, as England had little role OTL with the thirty years war. The collapse of the HRE's semi-centralized authority was more due to France and Sweden rather than the Netherlands and England.
One last thing; the succession. Don Carlos would be the heir apparent, but he's crazy and everyone knows it. But if he's disinherited the vast Spanish domains fall to Henry, unless Felipe tries to bypass him in favor of a son from a third marriage, which could cause an international war. So in this situation, Felipe might allow Carlos to marry, if only to gain male grandchildren to insure the division of the Empire (England and the Low countries and Spain and the Italian possessions) remains intact. I know this is a really long post and I do apologize for that. This is just a highly interesting POD for me.