Your best bet would be Copa airlines from LAX via Panama to Punta Cana or Santo Domingo. Alternativelly, you can fly from LAS with Continental to Miami or New York and connect to Copa there to Panama and DR, but the routing would not get you a cheap fare. Your best bet is Southwest to LAX and Copa from LAX to DR (PUJ or SDQ) with a stopover in Panama. Check Copa for fares and conditions, as many cheap fares will allow only a fly-through without stopover in Panama. Check fare basis and applicable fare rules and see under STOPOVERS to see whether a stopover is permitted. It will say either NO STOPOVERS permitted, or will say how many stopovers, and in what directions are permitted.
Also one trick:
Most airlines do not consider layovers of less than 24 hours as stopovers.
So if you get into Panama say at 10 am (scheduled) and leave to DR at 9.59 am (scheduled) next day you are not doing a stopover, only a layover. So if no stopovers are permitted on your fare, you may check into this. You would need to book a flight manually with Copa over the phone or with a travel agent (not online) as online services will not offer you these connections if the continuing flight is available the same day.
