I believe that certain genetic mental disorders or developments can definitely affect the IV and DV for Attachment vs Later Adjustment. Some examples of these would be aspergers, depression, or anxiety disorders.
Do you mean genetic disorders in the mother or in the child? For both cases, i agree, this could cause the child to attach to his/her mother in anxious/resistant or anxious/avoidance manner. If the mother has a mental disorder that makes her feel detached from her child, the child is less likely to engage in activities with his/her mother. If the child has a mental disorder, then they might be resistant to playing or exploring in the first place.