Suing him is not worth the time, money and headache. If her extended family believes him over her, a lawsuit isn't going to change that.
People seem to think filing a lawsuit is the solution to all their problems.. but in many cases, it's just the beginning. More than 200 years ago, the philosopher Voltaire wrote, "I was only ruined but twice: once when I lost a lawsuit, and once when I won one." His point -- that suing someone is just as stressful as getting sued yourself -- is even more true today than it was back then.
Slander is a form of defamation of character. In order to win a lawsuit, she would have to prove he lied about her and it damaged her reputation.
In this case, a defamation lawsuit would be a long, expensive process. Does he have money to pay, even if she wins?
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.