This is a long bow. First the conquest of Italy is not a likely occurence much less a given. The Italian mercenary defenders in Constantinople at the fall of the City were more than a match for the Ottoman attackers. Despite any political problems in Europe, the western states are not going to sit back and let the papacy be threatened by the infidel.
Further, the logistical problems of an Ottoman army landing in Iberia and proceeding to defeat a formidable military opponent is unlikely in the extreme. I doubt very much that any force the Ottomans were capable of landing in the Iberian peninsula could defeat any Iberian army at this time.
What seems to be missing here is why it did not happen in OTL if it all seems so easy. The answer is partly because the conquest of the remnants of the Byzantine Empire was being digested. The empires newly conquered citizens were still overwealmingly orthodox and not happy about being subjects of the sultan. Not much military force to spare for a foray against significant adversaries in Italy and the west. Foolhardy springs to mind.
I think maybe you should do a review of the history of the time. First, the Ottomans were not digesting the remains of the Byzantine Empire - it has long since ceased to be a factor and what little remained of it, the actual city of Constantinople, had been taken in the first year of Mehmed's reign, 30 years before he went after Italy (he was 21, so even in his early 50s there's no reason he couldn't have lived longer).
Second, the Italian mercenaries were
not more than a match for the Ottomans, they lost. Defended by massive fortifications in the most defensible major city ever built.
Third, even Charles V never attempted a field battle with the Ottoman army, because he knew he would lose, and badly. What was the Hapsburg response to Suleyman's move on Vienna? Run for the hills. (to Linz - not a stupid move, but also not exactly broadcasting confidence). And Mehmed's army has a greater technological and doctrinal superiority over Western armies than Suleyman's did.
There seems to be some thought that the Papacy exerted some magical pull on all Christendom. The relationship of the various Catholic nations with the Papacy were very complex and not altogether smooth. We're only a few years from the Reformation here.
The reason Italy wasn't taken was that the person interested in it died. Mehmed's successor, Murad II, just wasn't into military expansion, and the window of opportunity was lost as Spain was created not too long after.
I think this is the last TL involving the Ottomans I'll participate in. We never actually discuss a TL, it's just a group of people who say, "no way, the Ottomans suck". You're talking about an empire at the height of its energy and military advantage, that crushed multiple pan-European crusades and swept away all contenders virtually without reverse. Mehmed
did attack Italy, he
was successful in establishing a foothold, and the Pope
was convinced all was lost and made preparations to flee Rome.
I know everyone things Islam is some evil religion that everyone would resist to their dying breath, but that didn't develop in the lands conquered. First of all, the Orthodox population quite preferred the Ottomans to Latin rulers - the whole not trying to crush their religion and lack of exploitative and excessive taxation, not to mention security and effective government and all - so in Italy there are going to be plenty of people who accommodate themselves to Ottoman rule and are going to plain prefer it. The peasantry are going to have much, much lower taxes, a strong state can always coopt large segments of the nobility, and a peninsula divided into hostile city-states is not the best prospect for beating back a powerful empire. If you're say, Venice, and can accept Ottoman vassalage and thereby gain a huge advantage over your competitors, guess what? You're going to do it.
As for Iberian armies, good luck. United Spain definitely unlocked some major energies, but this is before that, and an Ottoman army operating out of convenient and rather wealthy bases in Granada is simply not a viable target for Castille and Aragon.
Nobody ever said this is a
likely scenario, we are discussing a
possible scenario. The
likelihood of a beylik centered on a little village in Asia Minor becoming a world empire in 100 years with 10 supremely talented monarchs in a row is pretty freakin' small, as is a band of Arabs overthrowing BOTH the Roman Empire and Sassanid Empires in like a year, as is a city state in Italy conquering most of the known world, as is a small tribe of horse nomads uniting Central Asia and sweeping across the entire Eurasian land mass, etc. That's history: fully of implausibility.
