The new chip cards are 'close to impossible to clone' - As more ATMs and POS locations in the DR incorporate chip readers only - then it will dramatically reduce cloning.
I suggest only carrying one card, and or your local bank ATM and have all the alerts setup to be notified of any withdrawals or charges - sent as text messages.
Keep your credit card companies numbers on your cell phone and freeze the account if there is unauthorized activity, or you misplace a card.
One thing is the charges here often appear to a name other than the business you used it - so it is sometimes hard to correlate.