I'm curious as to something.
Maximilian in Mexico wrote that his adoption of the two Iturbide princes was merely a ruse to either get one of his brother, Karl Ludwig's sons for the Mexican succession, or to get his brother, Ludwig Viktor, to marry a Brazilian infanta and their son would be viewed as the Mexican Prince Imperial (I'm figuring that this would mean Ludwig would marry Leopoldina rather than Isabel, or if marrying Isabel, a younger son).
How might a Mexican Emperor who's linked to the Brazilian Empire by blood affect history?
Did Maximilian really write that? Because it simply makes no sense. By the time he arrived in Mexico both daughters of Pedro II were already engaged to their fiances.
Anyway, even if they weren't already engaged, there would be no political support to such union. The Emperor Franz Joseph was against it when he first was informed of such plan (apparently he didn't want to waste Ludwig in South America) and, in Brazil, the Parliament was extremely opposed to even recognize the new Mexican regime, because they saw it as an European agression to the independence of a New World country. At the time, the public oppinion was incensed by the Christie Affair against what was seen as "British bullying", and the French intervention in Mexico frightened many that it could give European powers ideas that South America was free for the taking (remeber that 1864 was also the year that Spain took the Chincha Islands from Peru). The newspapers in Rio de Janeiro were claiming that the Mexican monarchy was doomed from the beggining, as "from New England to Patagonia is doesn't count with the sympathy of any people".
Also, there was the fear that aligning with the new Mexican regime could eventually lead to diplomatic troubles with the USA, causing the loss of a extremely important market for Brazilian exports (while Mexico simply didn't have anything to offer). Finally, due to the War of Paraguay, and the need to increase the government's budget in order to pay for military costs, the customs taxes were raised in Brazilian ports. Such measure could cause discontent among Brazilian trade partners, and so the government was very cautious to not cause sources of instability in diplomatic relations.