What is the ruling of Islamic law on performing a cosmetic nose procedure—whether surgical or non-surgical—if it is large and causes distress to the husband, and is likely to lead to divorce?

It is not permissible to perform a cosmetic nose surgery unless there is a disfiguring defect that repels people or causes pain and harm. However, if it is merely an ordinary large size that the husband dislikes, it is not permissible to reduce its size, because that entails changing Allah's creation, which is forbidden.