Hi Terry,
The double peak mountain with the cave is called Marvi and is an outlier south of the Psiloritis. It is possible to climb the Psilioritis (or Mount Ida) but not from the south via the Marvi. At least the hiking path ends at the cave.
The Psiloritis can be climbed from either the east or west flank. The view must indeed be fantastic. It would have been an option for me but I will have another dedicated hiking holiday later this summer and so I thought to take it a bit easier during my Crete trip.