my wife, from Santiago, and I live in Orlando and I constantly search for a cheaper more direct route. I've only been twice to the DR, and both were on American via Miami (once to POP, and then to the new STI) and both in the $400 area. :dead:
FLYPANAM.com shows flights from SFB to Santo Domingo, but the price isn't any better than AA. SFB is a small airport in Sanford, about 20 minutes north of downtown Orlando. The website lists STI airport, but doesn't seem to have regular flights.
I hope Viva expands since they appear to be based in Ft. Lauderdale, to FTL. That is about a 3 hour drive from Orlando, and a bit shorter trip than Miami. Flights from Miami are around $100 less, but you have to weigh in the 4 hour drive and parking your car.
Good luck, and welcome to Orlando unless you are a Yankee fan.