For hotels just Google Turtle Beach Resort and you may find going direct to source is cheaper, will also give you US hotel discounters (hotels.com) etc. Flights again have a look a virgin website just for flight otherwise not sure if BA goes there or try Jamacian Airlines - some of the charter airlines may go also - Monarch, Thompson etc - although they can be dearer than scheduled long haul.
Other flight option is to get flight into US and then buy one from US-barbados - Norhtwestern, Delta, United etc.
directly booking venue seems to come up at £3147 for the stay (14nts) and virgin flights are around 580 rtn per adult, so 4k may not be far off the price. Seems like its the resort not the flights that are racking up the price, althpough I am hungover and may be wrong about everything.
Two adults and 1 child in May for one week comes in at around £1500 on BA in World Traveller. That is the flight cost only. They can also do flight and hotels as a package. Worth looking at and BA can also work out a lot cheaper than Virgin!.