Dead Man's Island by Carolyn G. Hart is the first book in the Henrie O mystery series. It won the 1993 Agatha Award.
from the back of the book:
When arrogant media magnate Chase Prescott is nearly killed by a box of cyanide-laced candy, he dials his long-ago lover retired newshound Henrietta O'Dwyer Collins with a simple request: He'll assemble all the suspects if Henrie O will kindly point out the would-be-murderer.
It's a case-her first-that fills Henrie O with grave misgivings, especially when she arrives on Chase's private island off the South Carolina coast to meet the players in this deadly drama. Among Prescott's unstable young wife, his sullen stepson and his toady of a secretary, she has trouble narrowing the field of suspects-even when a second attempt is made on Chase's life. As Henrie O unearths a will and fascinating new evidence, a killer hurricane sweeps up from Cuba, threatening to maroon them in this vacation hell...where the trappings of luxury are put to lethal use and the secrets of the past have the power to engulf them all.
I won't be reading any more in this series. I knew who did it early on and knew the secret from Henrie O's past even earlier. She kept on listing the suspects and all the reasons why they were likely to be guilty long after I knew what was going on. The dread secret she did not want exposed seemed obvious to me. I didn't find the stunning revelations to be surprising at all.