Smiling, I'm sorry but I haven't read through the whole thread so I may be giving you some information that has already been put out there.
It sounds to me like a functional stability problem, likely in your sacroiliac joint. I just took a course this weekend on specific diagnosis of functional instabilities in this area and treatment. The treatment is very specific and requires a therapist that is familiar with the exercises. They are different than your standard pilates exercises but similar in principle. In pilates they have you work hard on your "power house" which is the equivilent of the transversus abdomenus contraction that we use in physio to try to get people controlling unwanted movement in the low back. Pilates also works on some of the larger prime movers of the hips (glute max, med, hamstrings etc) but it doesn't target smaller muscles around the hip and pelvis that we have more recently found out are really helpful in these types of injuries. The muscles that need to be targeted are often the deep sacral fibres of glute max, pelvic floor (sometimes this is counter productive), psoas (using an isometric compression type contraction), multifidus and the diagphragm. The hard part if figuring out which of these muscles does the trick and in what position. That takes some good evaluating and experimentation with exercise.
I'm going to see if I can find some helpful links to some of these concepts later today. I'm not confident tho, this stuff is pretty new. I'll be back.....
Living life like there's no tomorrow.
http://gorgebikefitter.com/
2007 Look Dura Ace
2010 Custom Tonic cross with discs, SRAM
2012 Moots YBB 2 x 10 Shimano XTR
2014 Soma B-Side SS