What should I do about my relative who falsely accused me of saying that my mother and her sister commit adultery, and claimed that her husband witnessed it, while my family believed her and disbelieved me?

Harboring ill thoughts about a Muslim is forbidden, and even worse is slandering them by accusing them of something they did not do. This is based on the Almighty's saying: ﴿O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin.﴾ and His saying: ﴿And those who harm believing men and believing women for [something] other than what they have earned have certainly borne slander and obvious sin.﴾

So, whoever slanders a believer by accusing them of something they did not do, Allah has threatened them with being made to drink from the "radghat al-khabaal" (the pus and fluid of the people of Hellfire) until they recant what they said. It is obligatory for whoever falls into this to repent and seek forgiveness from the one they slandered. As for the one who was slandered, they should be patient and seek their reward from Allah.