Is it permissible to seek divorce from one's husband after eleven years and three children, due to his lack of ambition, his constant blaming of the wife, his taking of her income, and his focus solely on the sexual relationship, coupled with the absence of love and desire to continue the marriage?

The fundamental principle concerning divorce is that it is abhorrent, and a woman is prohibited from seeking divorce except in specific circumstances. If it is possible for the spouses to reconcile and live together amicably, even through overlooking faults and compromising, that is preferable to separation. It is advised to discuss gently with the husband and remind him of his duties. If that proves ineffective, then weigh the harm of divorce against the harm of remaining with him, and choose the lesser of the two harms.