The US Civil War runs normally until August 1863, when the fictional nation Mexicatan (all of Central America minus the Panama islands) joins the CSA in invading the Western USA. Mexicatan is a puppet state for France, being a distant work around to Russia's threat of war if they get involve for the South.
With the help of Mexicatan, the Confederacy invades the Caribbean Sea in 1864. They succeed in taking over most of the islands, minus some that are closer to South America. Europe doesn't get involved because they are busy with more important things and none have a major stake due to lack of colonies.
The nations Deseret (Utah) and Second Nation (the Dakotas, parts of Nebraska, Wyoming and Montana) form, splitting away from the USA. Another fictional nation, the UAA or United Amazonian Alliance, (all of South America and the Panama islands) offers to help the USA, if they launch a successful campaign to reclaim the Caribbean Sea.
The UAA has a navy that rivals the British, with a large army that is highly trained, mostly against European tactics. In mid-1865, a book on how to advance their nation to 1930s era tech by 1868 is sent to all existing nations at the time.
The USA was able to get their hands on some additional blueprints that gave them a bit more of a technology edge over the rest, leading them to have 1910-era technology by early 1866 while the CSA only has technology equivalent to that of the 1890s.
In order to secure their new allies, both sides send their top Generals for the job to the Caribbean Sea. My problem is I'm not as familiar with the naval side of the Civil War outside of the Anaconda plan. I'm just looking at CSA, USA, and the French Foreign Legion for their best commanders to lead this campaign.