People have the right to speak their mind, but there is something else people need to realize. There are consequences to free speech. People also have the right to hold you to account for the things you say. So, while you have the right to publish unsubstantiated information about people, those people also have the right to sue you.
People should not be able to publish information on family members if it is not substantiated. Being a family member of someone should not make any difference because many families do not get along. The internet has made it very easy to publish unsubstantiated information on anyone with relative ease.
I do not agree with people being able to publish information about people that is false because if the information is not valid then anything said about that person that has been published is a lie if you can prove that someone did something dont accuse them of being wrong.
People should not be able to publish information about their family members, especially if the information is unsubstantiated allegations. This information does no good for family relations, and even worse it can expose a person's personal life and reputation for millions to see. Doing so online can bring a great deal of stress to the life of the person spoken about.
No, I do not think that you should ever take info about a family member and publish it somewhere. I think that you need to respect your family and keep them and their business private from the whole world so that you can keep a good relatioship with them forever.