See
http://dr1.com/travel/puntacana/
Dominicans are friendly and will be kind to your twins. The DR team does well in the Olympic Games for special needs, so our contenders with down syndrome have gotten their share of good exposure.
Cash your dollars as you need. The better rates are to be had in the exchange houses. You may consider bringing travel checks, to not travel with much cash, but you will need your passport.
For many items you may pay in dollars, for others you will be better off paying in pesos.
Read through the helpful information in the travel section of this site.