Even if you expose this information to your family members, the only remedy for your father would be to file for divorce.
But given the fact that he’s mentally not fit at the moment, he cannot file a case or even give testimony.
You must consider the overall picture of the family. Is your mother failing on her duties towards the family? Is she planning to divorce your dad and go with the other man? You need to have an honest conversation with your mother first. Once you involve other family members, it’ll just become a shit show and name calling session.