Must the questioner remain with her husband who wrongs her, and for whom she harbors hatred, given her mother's refusal of her request for separation?

If by "writing the book" the marriage contract is meant, then your cousin has become your husband. You must obey him and treat him well, and he must observe your rights and treat you kindly. If you strongly believe that the situation will not improve, you may request a divorce from him. If he refuses, you may return the mahr (dowry) to him in exchange for khul' (divorce initiated by the wife), provided he also agrees. However, if the matter is merely an engagement, you may dissolve it if you fear neglecting his rights and failing to observe Allah's boundaries between you. In the event of reaching a dead end, it is advisable to refer the matter to the Sharia (definition) courts.