So, assume that Spain after Napoleon's departure manages to maintain control over most of its Latin American colonies, through a succession of factors such as José de San Martin's Army of the Andes failing to liberate Chile, Simon Bolivar either being crushed early or confined to Venezuela, and the Spanish army at Cadiz not revolting under Rafael del Riego.
For a second point, assume Ferdinand VII still has only daughters, and still doesn't want to give the throne to his brother, Carlos of Molina. The First Carlist War for the succession to the Spanish throne still happens.
I ask, how will Spain's American colonies react? Who will support Isabella, and who will support Carlos? Would the carlists make overtures for Latin American autonomy, like they had promised to the Basques and Catalans IOTL? Would there be a division of loyalties between each colony?
 
My guess would be whoever would give Latin America mestizos and natives the most benefits.

From purely what i know, Carlists would have an advantage by virtue of their beliefs of respecting regional cultures and local autonomy.

If they made concessions about respecting the cultures of the mestizos and the natives along with the autonomy, they would probably support more the Carlists for the time being
 
The question becomes what's left of the OTL revolutionaries and how the Independence war was lost. Do they still have an appetite for independence or liberalism? At first glance, I'd say most of the sympathizers with the defeated revolutionary cause would side with the liberals - but there might not be many of them around after their defeat. OTOH, although absolutists, the Carlists may win them over if they concede on regional issues, as @CountDVB said. But it's also perfectly possible that the region is dominated by peninsular armies and that the former leaders had been executed in brutal ways, so the appetite for rebellion may be lost and as far as Spanish America is concerned, it becomes a matter of regional issues rather than liberalism vs absolutism as the independence wars were about.
 
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