Is swearing falsely on the Qur'an twice to clear my name—with the good intention that my sister not follow me into error—considered a "yameen ghamoos" (a false oath taken deliberately to seize another's right or property)? What must I do for my repentance to be accepted? And must I tell my sister the truth, despite the problems it might cause?

Whoever falls into sin must conceal himself and repent sincerely. It is not permissible for him to inform others of it. Lying is forbidden except out of dire necessity. The matter becomes worse if an oath is added to it, and even worse if it is sworn upon the Mushaf. There is no expiation for an immersive oath (yamin al-ghamus) according to the majority of scholars; rather, repentance is obligatory for it. Some scholars, however, are of the view that expiation is obligatory.