Dear Community

I have a question regarding baggage rules on different airlines with short stopover. I have a flight with AA flight number from Quito to Miami BUT operated by LAN. This flight is part of of a round the world ticket offering me 2x23kg checked luggage. One bag is a surfboard, which is not a problem for LAN as it's an exception and just counts as part of normal allowed luggage weight. So I can check my normal bag and my surf board for free.

Landing in Miami, I have a 14h stopover and then a separately booked flight with US Airways or AA to Puerto Plata. This ticket is bought separately and not part of RTW ticket. It only allows me to bring hand luggage. Surfboards are normally +150 USD for US or AA because of oversize (unfortunately not as nice as LAN)

Do I have to pay for the luggage for flight from Miami to Puerto Plata or can they check my luggage through from Quito to Puerto Plata and I don't need to pay anything? Remember, the tickets were sold individually, and I have 14h stopover in Miami.

Thanks for your help
Cheers