You note lax ligaments. These should be able to be demonstrated with x-rays at endpoints of motion. The motion of one side should be much greater with subluxation noted of the joint as compared with the other side. Occasionally with a CT scan at the endpoints of motion, this instability can be demonstrated.
Most times, it is not ligamentous hypermobility but it is facet or nerve inflammation that causes symptoms. Diagnostic blocks of these structures (see SNRB or facet blocks on the website) should yield temporary relief and treatment is based upon the disorder discovered.