Nope, they are liberals but not republican. As bad as the king was, they only aspired to "open his eyes" and convince how wrong he was and how well would be the country if he listened to them... And the fact of having a king or queen behind them gives them some legitimacy and possibly gets away a foreign intervention to destroy them (something that happened anyway in '23, though).
Alright I agree with what your saying. If Carlos were to wage a much more successful campaign for the throne though, could we see the liberal opposition morph into more radical republicans, either as the moderate liberal elements accept Carlist rule, or the brutality with which Carlos rules drives the liberal to violent opposition?
Spain is the homeland. Even as rich as the colonies are, ruling them while the homeland is "in peril" is pointless in the mind of a monarch of the time. That's why Carlos is not going to leave Spain without trying to place it back in the fold.
Isabel could end in exile, or in any retirement house in the country, or even married to one of Carlos' sons (he planned this at the end of the First Carlist War, when it was evident that he could not achieve victory on his own). Her supporters could be victorius as IOTL too, though. But in any case it is sure that Carlos is not going to leave the issue without trying something.
With Carlos ensconced in Mexico with his native conservative supporters, I think that a marriage may make much more sense. Carlos could continue to rule in Mexico, one of his sons (I would say his older one) could go to Spain, and the Spanish Empire (at least the Spanish and Mexican parts) could stay de facto united. Carlos could designate his eldest son (the King of Spain) as his heir.
[/quote]The Southern Cone is probably gone at this time, though. But New Granada could have been subdued again. It all depends of how many cooperation between the Mexican and Peruvian monarchists is there and how successful they are in cooperating to suppress the rebellion there. Plus, the fact they are with their hands full trying to defeat Bolívar and their own revolutionaries would explain perfectly why Carlos&Francisco don't really intervene in Spain in 1823.[/quote]
If you have this happen, then the Royalists in Latin America basically now look to Mexico City and Carlos for leadership, while Spain could continue to supply troops. I think that the Wars of Independence were close enough run things that with Carlos in Mexico City New Granada, Peru and Mexico could be held. Rio de la Plata might be beyond the effective control of Mexico City or Madrid, but I think that fraternal bonds could mean that Argentina would be happy with a Carlist prince (I believe OTL Argentina was also in the market for a monarch).
If you have Carlos and co. in Latin America with the Wars of Independence ongoing, I think that there is a very good chance that there would be an American intervention. The Americans do not want the Spanish to continue to hold most of Latin America, and would feel ideologically allied to pro-independence republicans like Bolivar. The British were quite supportive of the Latin American juntas and supported independence movements, and were also concerned about continued Spanish rule in the Americas.
Could we see a joint Anglo-American intervention in the Wars of Independence? I'm thinking the British basically blockade the Americas, preventing further support from Europe, while the Americans directly intervene in the Wars of Independence. American troops land in Cuba, and American "volunteers" go to support Bolivar in New Granada. Carlos would be able to maintain control in Mexico, but in New Granada, Peru, and Argentina the pro-independence movements prevail.