Final answer:
The man's symptoms and family history suggest Huntington's Disease, caused by the expansion of CAG trinucleotide repeats on chromosome 4.
Step-by-step explanation:
The likely cause of the disease in a 42-year-old man with a family history of a movement disorder and uncontrollable movements is Huntington's Disease (HD). HD is characterized by involuntary spastic movements and difficulty in controlling voluntary movement, which often presents along with cognitive decline. The cause of HD is a mutation resulting in an expansion of CAG trinucleotide repeats on chromosome 4. This genetic anomaly leads to the production of an abnormally long version of the huntingtin protein, which eventually causes neuronal cell death and the symptoms observed in the patient.