Is there any movement to unite the Spanish American countries into one republic?
Republicanism isn't popular ITTL, that the only example of a stable republic is a very racist and segregationist country like the United States is not very good propaganda. What had become popular are the socialist movements
 
Is there any movement to unite the Spanish American countries into one republic?
A nationalist movement perhaps ...

Although instead of being a single country, it can be a federation of countries. A kind of European Union under the same monarch (with power in Spain and constitutional in other countries, and later only constitutional) and a common army (instead of NATO).
 
And the relationship between Mexico and the USA?

Surprisingly very friendly, despite the fact that they are completely different countries (America is an Anglo-Saxon, segregationist, Protestant and Republican country while Mexico is a Hispanic, mixed-race, Catholic and monarchical country) these differences help the United States a lot in the task of avoiding arrival of Catholic immigrants from Europe.
 
I decided to put the provisional capital in Lima because, if i recall correctly, the regions of Lower and Upper Peru was the most profitable and important of the Spanish America

Not sure where your information was obtained, but from looking a books from the period, New Spain produced far more revenue and silver than Upper and Lower Peru combined, and had done so since the 1670s. In 1804, the Spanish Crown collected 36 million pesos in revenue, with 62% coming from the Viceroyalty of New Spain, 16% from New Granada, 11% from Peru, and another 11% from La Plata.

Going to Lima would also have been an insanely long and dangerous voyage. The trip in ideal conditions would have required sailing two months from Seville to Portobelo and another 2 weeks sailing through the Chagres, where it was very common for sailors to die of fever. From there they would be sailing against the Humboldt Stream which could take another 3 months and ideally done from September till April. The other option would be sailing to Cartagena and going by mules to Lima which would take several months.

By contrast, Sevilla to Veracruz took about 2.5 months with another 21 days overland to Mexico during dry season and 31 during the rainy season. Neither would be ideal, but one can see why Ferdinand originally sought refuge in New Spain.
 
Not sure where your information was obtained, but from looking a books from the period, New Spain produced far more revenue and silver than Upper and Lower Peru combined, and had done so since the 1670s. In 1804, the Spanish Crown collected 36 million pesos in revenue, with 62% coming from the Viceroyalty of New Spain, 16% from New Granada, 11% from Peru, and another 11% from La Plata.

Going to Lima would also have been an insanely long and dangerous voyage. The trip in ideal conditions would have required sailing two months from Seville to Portobelo and another 2 weeks sailing through the Chagres, where it was very common for sailors to die of fever. From there they would be sailing against the Humboldt Stream which could take another 3 months and ideally done from September till April. The other option would be sailing to Cartagena and going by mules to Lima which would take several months.

By contrast, Sevilla to Veracruz took about 2.5 months with another 21 days overland to Mexico during dry season and 31 during the rainy season. Neither would be ideal, but one can see why Ferdinand originally sought refuge in New Spain.

And you're right, it's something I realized later, having put the provisional capital in Lima instead of Mexico was the only nonsense in my story.
 
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