Can I sue a relative for deformation of character?

Defamation can be hard to prove in court. You probably need counsel ( I do not do these cases). Certainly send the family member a written certified mail notice of what they said, why it is false and demand they delete the false statements or you will take action and demand damages and attorney fees. It helps if you have actual proof that what is being said is false. Remember, opinions are not actionable.   Good luck