Judy, we took the Private Apartment of the Kings tour this September and can't recommend it highly enough. Small group (25-30 max I think?) and you get an audio set so you can hear the guide perfectly. Great tidbits of information and gorgeous rooms. Hang to the back and you'll get to enjoy them all to yourself for a minute before moving on. When the tour is done, you get dropped off in the palace just before the major attraction rooms (like Hall of Mirrors) and tons of people. Seeing the private rooms in such a quiet, people-free setting almost ruins the experience of the regular public rooms. :)
Yes, you do get to skip the long security line with this tour.
Looking back, my approach would be to book the Private tour for the latest time slot in the afternoon. I would get to the palace as it opens, and explore the gardens and grounds. I would head to the Petite Trianon for it's opening time, and after visiting it, head to the Hamlet. I would then go to the Trianon (we missed it this past visit) and eventually head back to the palace for our afternoon tour. It takes a REALLY long time to walk from the Palace to the Petite Trianon since the estate is so big. In hindsight, I would have bought tickets for the little train that runs around the estate. They wouldn't let us buy tickets by the Trianon; I guess you can only buy them right at the Palace? Others may know more about that.