Fedex is reliable as is UPS from Punta Cana. I have used both of them. There are a few places to send from. I use EPS located in the Plaza Riviera Mall on Ave. Espana. They will send it for you. Cost is high though, but it will get there in 2 or 3 days at the most.
As far as coming into the DR, I have had no issues with that either. May take one more day than going out but totally reliable. Just have a reliable delivery address, such as an EPS office.
WW - we found the same thing -Guaranteed three days to Europe. Nope -it took an extra day and did not meet the FedEx schedule. It was sent from EPS in Sosua and they said three days to Europe. It was not !!! Perhaps we can claim on FedEx for missing their schedule!!
Olly and the Team