Good luck on understanding US documentation rules. Being a US citizen is one requirement, another for new documentation is establishing a validated trail of ownership back to the builder. This trail may be difficult or impossible to create if a vessel has changed hands a number of times or if the builder is defunct. My suggestion would be to talk ($$) to people who specialize in documentation services found at http://www.americanvessel.com/us-map.htm
USCG documentation may be a requirement for financing and/or insurance, depending on the where you live and how the vessel is to be used.
A 36 foot vessel on the Atlantic willl get very small, very quickly. Based on your questions, you sound new to the game, you might want to get some experience before considering a trip back from Latin America. Should you proceed, I'd suggest looking for a US vessel for sale in Latin America, already documented. Sometimes cruisers get half way and decide that's enough... and usually the seller is quite eager.