The atlanto-axial joint is the joint between C1 and C2, these are the top bones in your neck, so if head movements are causing subluxation here, that means you have a degree of cervical instability between these bones.
The head and neck should move as one unit, so if one bone turns, the bone below it should move correspondingly. In your case these two bones are moving independent of each other to some degree, causing problems.
More importantly, I have looked at your MRI and have annotated it below because I think you have a problem at the craniocervial junction too (between head and neck, or C0 – C1). Just looking at the distance between the bottom of your skull, at the back and the top of C1, at the back, the gap seems too wide. Have you been in an accident ?
Regards
Barbara
(UK)