Because you will used two different airline probably need to change terminal and so need to do immigration and customs in US, after need check in your luggage and flight in American counter to flight DR. Try to have enough time btw connection. Miami airport is complicated and difficult. But it your travel only using one airline from beginning to the end, both legs using American Airline, probably don't need immigration and customs in US, just in DR. Just change gate in Miami airport. Good Luck...
No you have to get your luggage and also have to go through customs/passport control.
All passengers entering the US go through the same international arrivals process, even if you are transiting from one country to another. You will claim your bags before exiting the customs area. Since you are flying on two different airlines you will need to go to Concourse D and check in your bags with American Airlines before you can proceed to TSA security so you can get to your departure gate for the Dominican Republic. You can find more information here: http://www.miami-airport.com/international-travel-arrivals.asp
You need to claim your luggage/s. And checked in again. .
I'm pretty sure you will definitely need to claim your bags and recheck them as well as go through Customs and TSA again. It can be very intimidating and overwhelming if you aren't used to it. Definitely make sure have time, just returned from an international flight where the two hr layover was actually the time it took to claim/recheck and pass security and still get to my gate. Alot of this time includes walking across the airport.
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