DBWI: A united Mexico?

Mexico is one of the great what ifs of the post-colonial Americas. Assuming Mexico had been able to get a hand on the political instability of the brief republic period and hadn't splintered into individual states throughout the 1830's how does the nation progress? Presumably they'd be a major player in the Americas?
 
Are we also assuming that Peru, New Grenada, and Brazil stayed unified as they had under Spanish and Portuguese rule? Though I guess it does come down a bit to if we consider the Braganza, Habsburg, and Bourbons spread around the Americas as continueing there legacies. I mean mean New Spain had what... seven kingdoms in it at first? Guatemala, Mexico, Yucatán, the New Kingdoms... you need to do something about the natives if you are to keep the area unified. A good amount of them went Catholic, but nationalism (not regional identity, that's only counts if you aren't in your own country) was for the tribes and their heirs that survived Castilian, Aztec(the others haven't forgotten how they as the ancestors of Mexica), Apache, etc despoliation son their own. Maybe have then unify against the invasions by the Italians in that farce of a war?
 
Would the USA have taken as much of the old Northern bits of Mexico and New Spain had it faced united opposition, as opposed to annexing large swaths, with others like Texas or Rio Grande outright joining the USA?
 
Would the USA have taken as much of the old Northern bits of Mexico and New Spain had it faced united opposition, as opposed to annexing large swaths, with others like Texas or Rio Grande outright joining the USA?
The Texas and Rio Grande that are part of the gulf to gulf Frontier Confederation?
 
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