Is it permissible for the sister to leave her fiancé (her maternal and paternal cousin) after seven years of engagement and عقد قران (marriage contract), even though this may cause major disputes and her parents to lose their standing among people?

If "writing the book" refers to the legitimate marriage contract, then the woman has become the wife of her maternal cousin, and she does not leave the marriage except through divorce, which is in the hand of the husband. If the woman requests a divorce because she knows she will not uphold her husband's rights and will not observe the limits set by Allah, then she is permitted to request a divorce without compensation or with compensation, and this is khul‘. It is recommended for the husband to grant her request, and family problems should not be stirred up. It is advised to be deliberate, study the matter, seek guidance from Allah (istikhara), and consult with family, as the dislike might be a fleeting feeling that will pass, and affection and mercy might ensue.