Tom--
You are describing the correct Palm Beach Country Club. You keep driving north from The Breakers on County Road, the road all of sudden makes a hard right bend and a quick left bend about 2 miles up, you are there. Good luck getting in the entrance during the winter, especially now.... It's hyper exclusive, even more so than Everglades, but probably equal with Gulfstream Golf Club.
You are correct in describing it as almost exclusively Jewish, however I believe the Kennedy's were members there. The former Kennedy compound is nearby from what I understand. If you want some more details about the club, email me...adammessix@aol.com.
It's definitely worth the opportunity to see if you can get on.