In 1510, the theologian and philosopher James of Athelhampton had written a text "About the divine right of the king", propagating that the king should stand higher than the bishops in his lands. This basically meant a breakaway from the pope in Avignon. Since he had abandoned Rome, many Christians had criticized him; and since more and more money from the Quadruple Monarchy's lands in Africa and Atlantis went into his coffers, the number of critics had grown even more.
The English nobles accepted the proposal after a few months, but Castille-Portugal was more reluctant to accept the king as head of church. The coalitions formed in this religious dispute didn't even ask for nationalities, classes, or even families. From 1511-17, the Iberian peninsula went through almost Civil War-like conditions. The opponents of the king were rewarded with the property of his defeated enemies (including some church property), which helped him to succeed. He founded the "Occidental Christian church".
In 1514, the French regent François was crowned Holy Roman Emperor Franz I (in Avignon).
1519, after a meeting of the cardinals of the Quadruple Monarchy, they officially accepted king Edward V as supreme spiritual authority. The liturgy or anything else substantial wasn't changed. The Occidental Schism began. The church property in the Quadruple Monarchy went to the king as well, who gave it to his followers, thus further strengthening his authority. When the pope protested, the king declared in return that he wouldn't accept the authority of "the lackey of the French king".
In 1521, the only surviving heir of the Norwegian (and Scottish) throne, Prince Alasdair / Alexander went to Atlantis, where he spent some time around the Caribbean. He also approached the Tenochca and learned about their gold riches. One year later, he came to the court of France, to warn the king that the Quadruple monarchy was about to conquer the rich lands of the Tenochca. He pointed out: "If the king owns their gold, he can afford to hire all the mercenaries in the world! You have to stop him now!" The king was convinced by his reasons, and decided to start the war. Time was short, in fact: 1523, when the first battles happened, the Castillians wanted to send an expedition to Tenochtitlan, but the ship from Cuba was destroyed in a hurricane, and until replacements were found, the necessary time had passed.
The war in Atlantis
France managed to smuggle some hundred soldiers and advisors to Atlantis in 1524 to help Cuitláuac, the military leader of the Mexica, as the Tenochca were now called in Europe. The Tenochca had to convert to Christianity, however. Luckily, the French hadn't come too late: In the battle of Cempoala 1526, the French-Tenochca defeated the Castillians.
1529, a smallpox epidemics hit the Mexica... however, the allies of the Quadruple monarchy weren't better off, so it was a two-sided damage. The disease also killed Motehcuhzoma II 1532, and Cuitláuac becomes new ruler of the Mexica.
In 1535 however, the Castillians drove the French-Tenochca back to the heart of the old Tenochca Empire, allied with their old enemy Tlaxcala. Only the lack of support prevented them from winning completely.
1545, in the battle of Ile de la Tortue (OTL Tortuga), the French defeated the English-Castillian fleet again.
The war in Europe
1527: Although the war on land went well for the Quadruple monarchy, where the new Castillian tercios repeatedly defeated the French, their fleet was defeated in the big sea battle of Biarritz.
After the defeat of Cempoala 1528, the war in Europe intensified. The Quadruple king hoped for a reconquest of Aquitaine. France felt threatened and needed a diversion. So "Prince Alasdair" who had returned from Atlantis landed in Scotland, soon gained followers, started a guerrilla war against the English. In 1530, the Scots defeated the English at the battle of Stirling, reconquered the Lowlands.
In 1534, Charles VIII was elected king Carles of Aragon. Now this country entered the war too on France's side, giving Castille a wide open flank, which France used to its advantage.
After the death of emperor Franz 1535, king Charles was elected new Roman king Karl VI, despite some resistance (he only got six out of nine votes). The HRE stayed in the war.
During 1538-42, uprisings in Morocco started. The rebelling Muslims were enslaved and mostly brought to the New World. However, they distracted the Quadruple Monarchy, which had to move Castillian troops from France to Morocco.
After Morocco was secured in 1543, the insulted Quadruple king wanted to get rid of Prince Alasdair, so he moved his troops not to Aquitaine, but Scotland. The Castillian and Portuguese troops weren't accustomed to the land and the climate, which weakened them.
After several indecisive battles, in 1546 Prince Alasdair decided to let the troops of the enemy march deep into the Highlands, making them believe they were chasing the Scots. As the chronicles wrote, certainly no other Scot leader would have been able to demand that of his people - which proved Alasdair's charisma. He didn't disappoint the Scots: At October 10th, they destroyed their enemy in the battle of Callander.
Other events during the war
Since the two greatest powers of Europe were bound in a war that some people in TTL call the First World War, smaller powers had the opportunity to expand in Atlantis, and took it too.
1528, king Henrik of Scandinavia took advantage of the war, acquired the islands of OTL Virgin Islands, Anguilla, Saint Christopher and Nevis, Antigua and Barbuda, and Montserrat for his empire.
In the same year, Huascar, son of Huayna Capac, was caught conspiring against his brother, the heir of Huayna Capac, named Ninan Cuyochi.
1531, the Dutch founded colonies on Guadeloupe, Dominica; and 1533, Braunschweig-Lüneburg claimed the islands of Martinique, Santa Lucia. The Florentines took Saint Vincent, Grenada and Barbados (which they called Elba Nuova) 1536. Poland joined the colonial powers in 1539, took Trinidad and Tobago.
In 1543, with Scandinavia in Civil War / unrest, the other powers used the opportunity. Nystad, the capital of New Sweden, was taken by the Dutch; the South and West of the Chesapeake peninsula went to Italia Nuova. The Netherlands and Florence made a treaty, ruling the border between their colonies in Atlantis, and promising to respect their borders. And when in 1544 in Haraldsborg, the (almost) last Danish colony, chaos ensued, Poland sent soldiers to the city, occupying it. Haraldsborg became the portal for Polish and Prussian immigrants to (Northern) Atlantis.
Despite the war, exploration of the New World continued. 1530, the Castillians explored the north coast of OTL Colombia and Venezuela, discovered the Orinoco mouth, occupied the Antilles, and built first settlements in South Atlantis. In 1538, they crossed the isthmus of Panama, discovered the Pacific. They also learned about the lands of the Inca.
Said Inca conquered the Chibcha lands in OTL northern Colombia during 1541-50.
1547, peace was made. The Quadruple Monarchy had to cede Murcia to Aragon, and accept the independence of Scotland-Ireland under Alasdair / Alexander IV in Europe, and of the Mexica and Inca people in Atlantis (who had to convert to Christianity, though, since the pope insisted). Plus, they had to pay several tons of gold. In Atlantis, the Quadruple Monarchy ceded West Florida, Panama and the Mississippi valley to France, and western Anderland to France's ally Denmark.
Before the war already, in the 1520s, a new Christian movement spread through Great Britain, as a reaction to king Edward's Caesaropapism: The "Independents", who demanded that the state should completely stop interfering with the church, and again demanded the translation of the Bible, which the church still declined. After the war, many of them were imprisoned or exiled to New England.
By breaking the union of the Catholics, king Edward V had broken a dam: 1535, king Henrik VI started the Scandinavian church, confiscated the church's property and had the Bible translated. Other states like Poland followed suit.
After the end of the war in 1547, Europeans started regular trade with Mexico and Tawantinsuyu (the Inca empire). They kept their independence because neither great power wanted the other one to own their rich lands.
1549, the double revolt in the (now) Triple Monarchy of England-Castille-Portugal happened: Both the parliament in England and the Cortes in Castille forced the king to resign, made his more popular son Edward VI king.
Prince Alasdair went on not only to take the throne of Norway, which he had inherited after all, but also those of Denmark and Sweden, giving those countries peace and stability. Towards the end of his life, he even was elected Polish king and Holy Roman Emperor, for a short time having half of Europe under him.