Headaches certainly can develop from instability of C1-2. If you have an atlanto-dens interval (ADI) of 5mm or greater, you have instability by definition.
There are no exercises that can help an instability like that. You will probably need a fusion. Make sure that the occiput-C1 level is normal without instability here too.
Donald Corenman, MD, DC is a highly-regarded spine surgeon, considered an expert in the area of neck and back pain. Trained as both a Medical Doctor and Doctor of Chiropractic, Dr. Corenman earned academic appointments as Clinical Assistant Professor and Assistant Professor of Orthopaedic Surgery at the University of Colorado Health Sciences Center, and his research on spine surgery and rehabilitation has resulted in the publication of multiple peer-reviewed articles and two books.