O.k. just a thought.... Maybe once you go past parallel your gluteus and piriformis are overly contracted or even tight to start with so when you get to that point you are putting it into a stretched position. When you first go down you are using the hip flexors as a prime mover and glutes as a synergist. Once you go pass parallel your glutes begin to stretch and start pulling on your greater trochanter. Your deep lateral rotators could also be overly concentric to begin with and you could also be aggravating them.
I'm going off on a limb and saying muscle imbalance and instability in the joint.
So once you hit parallel, you are saying muscles are pulling on the hip joint to make it feel like it is coming out.
The only things that I can think of attaching to the greater trochanter are:
Piriformis, quadratus femoris, gluteus medius and minimus, Superior gemellus, Inferior gemellus, Obturator internus and Obterator externus. Then you also have iliofemoral ligaments in there. I would think though if your hip was double jointed that the ligaments would be loose and you would hear snapping even when you walked.
Lesser trochanter is the psoas but I rarely if ever heard of a psoas weakness.
Here's a piriformis and glute stretch:
http://www.rice.edu/~jenky/sports/piri.2.html
http://www.exrx.net/Stretches/GluteusMaximus/LyingModified.html
I would also watch your feet positioning. Make sure your toes are pointed straight ahead so you are not activating the deep lateral rotators.
You can also test this concept by doing seated hip extensions. If you put a heavy enough load on and when you extend your legs your hips and butt want to come off the seat then your hip flexors (psoas, quads, sartorius, TFL) are overly tight and you need to stretch them more often. Try and do the hip abduction machine and see what happens then. If you feel the same pain in your hip then your gluteus medius is overly concentric and you should work on stretching that muscle along with your piriformis. I would find out what the muscle imbalance is before I would even bother with doing any strength training and possibly injure yourself.
IMO