From what I've read, Brazil had always looked to the US as a leader and model due to their similarities (large country/population, slavery, start as an European colony to independence). Brazil supported the Confederacy in the war due to the slavery aspect (US abolishment was 1865, Brazil abolishment was 1888) and the actions (or non actions) of the US in various Brazilian events, which increased political tensions for years to come.

The book Brazil and the United States by Fontaine states, "Brazil adopted precisedly the same position the US took during the 1817 Pernambuco (port city in Brazil) revolt, neutrality, which meant it accepted the belligerent status of the Confederacy. In doing so it followed the lead of the European powers. The US tried to prevent the Confederacy from obtaining any advantage from a neutral power. But the American chargé in Rio was so clumsy that US interests, even in the absence of southern agents in Brazil, were not advanced. Brazilian-American relations thus remained badly strained until well after the war."

Sorry for any typos, on mobile and about to sleep. I know this only covers Brazil and the US but hopefully you get some more answers.