I can clarify the situation - both the Valley and Dunluce are indeed operated by the same body - that is, the membership of Royal Portrush, spearheaded by the Secretary Manager Wilma Erskine.
The Valley has it's own clubhouse and membership, and is called Rathmore - these members can play the valley course, but not the Dunluce. If you are a member at Royal Portrush, you can play either course.
Essentially, the lady members of RPGC play much of their golf on the Valley course, and the men play all events on the Dunluce links. In fact, if you stand on #18 tee of the Dunluce, you are standing next to the Ladies clubhouse (yes, they have their OWN clubhouse). On the other side of that is Rathmore clubhouse, which is the working mans Royal Portrush, for want of a better term of explanation.
Hope this clears it up. Oh, and by the way, Darren Clarke loves to play as much of his golf on the Valley as he does on the Dunluce when he is in town, and Graham McDowell, the new rising star on the Euro Tour played ALL his golf at Rathmore - his Dad is a schoolteacher, and could not afford the lofty fees at RPGC.!