I don't think balkanization of the aztecs could occur since thier empire was not cetralized at all, i would be more like a kingdom losing control of its principal noble or them turning into warlords. Aztec's was never an empire in the typical way, moreover, their governing structure was contructed from the union, IIRC, of noble families or similar tending to a council. The power was distrubuted from the middle of that. A structure created from a combination of other smaller ones rather than a system imposed from above.
What is popularly known as the Aztec Empire was actually a triple alliance of three city-states and their nations/tribes (the Mexica, Acolhua, and Tepaneca who ruled from Tenochtitlan, Texcoco, and Tlacopan respectively) who together created a hegemonic empire they shared the leadership of. Well, mostly shared, Tlacopan only got 1/5th of the tribute whereas Tenochtitlan and Texcoco each got 2/5ths and Tenochtitlan was able to exert more power and influence thanks to their larger population and bigger army, as well as the fact they controlled the important trade city of Tlatelolco. Still though, the Tepanecs and Acolhua were still considered equals of the Mexica. And leadership of each city wasn't exactly a family-run oligarchy of the form you describe, though nobles maintained all the important positions and were often if not usually related to each other. The Huey Tlatoani was the paramount leader, with the Cihuacoatl as the sort of second in command and in charge of mostly domestic issues, like a sort of vizier or prime minister. Then there was the advising council of four generals. The tlatoani generally filled these slots with relatives and upon their death they'd choose someone among them to be the next tlatoani. So it wasn't really a hereditary monarchy, but yeah, it generally ran in the family.
I'm well aware, but while conquest wasn't pre-ordained, disease sort of was. I'm not an expert on diseases and how they transfer, so I'm not sure if there's a chance to avoid that mess, but if it's there, then absolutely a POD in the Americas themselves would be awesome indeed.
The problem is that saying that the diseases were the biggest factor in the colonization of the Americas, while true, is an extreme simplification that tends to make people blind to what really happened. The existence of these diseases and the fact they killed millions doesn't mean that the Native-Americans were a doomed people as long as smallpox and the like existed in the world or they didn't have their own version or whatever. I find one of things AH.Commers get wrong is that history isn't composed of grand movements and deterministic themes or whatever. People here seem to too often forget that history is human.
There are so many little things that could be changed without being drastic like saving prehistoric megafauna (not to say twovulture's TL isn't good) or what have you to avert colonization, at least in specific events. What would happen if the slave girl Malinalli wasn't given to Cortez among the other gifts from the chieftains in Tabasco? Without a loyal translator willing to screw over the Mexica, how could Cortez take over the Aztec Empire? And if his expedition was seen not as a triumphant example of how adventurers could topple native empires to claim riches, but instead the third catastrophically failed attempt in a row, the impetus for colonization in the Americas takes a massive blow. People aren't as excited as gold and riches anymore, and people will be far more cautious or skeptical as to their chances of survival should they try to strike it out as some sort of conquistador. It's a ripple effect and it can't be ignored, humans aren't robots who during specific eras were programmed to destroy and plunder without regards to their own survival or success.
And another point, people here seem to ignore that the Americas have their own history before Columbus, or so it would seem as most people seem so extremely hesitant to have a colonization POD that occurs in American history rather than European or Asian history. Things happened in America that given the right ripples would result in a massively different New World that the Europeans couldn't exploit the way they did IOTL. It doesn't have to be extremely grand either. Change the result of a single battle in Maya history that took place in the year 695 AD, and you could avert a catastrophic social collapse that happened over a hundred years later, prolonging the highest period of development in the Mesoamerica region which would likely result in a much stronger (and different) Mesoamerica come 1500, and since European history wasn't changed it'd still be the first place on the mainland visited, which would change the way America was colonized to be sure.
I was originally thinking of a later POD than being discussed here, closer to 1600 or 1700 than the Spanish conquest of the Americas. BUT please keep the Inca/Aztec discussion going! I find it interesting
Going by that era, having the American Revolution fail would probably help the Iroquois a lot, or at least the tribes that supported the British. They didn't all help the Brits so that might lead into some troubles. Going the other way, I wonder if some tribes would be given the same sort of independence owing to their alliance with France should the French and Indian War end differently. France had their own native allies who could possibly exert more independence at the expense of the British colonists in America should the French win.