What is the ruling of Islamic law concerning a wife whose husband is unable to fulfill her marital rights, and is it permissible for her to seek someone who can meet her needs outside of marriage, especially given the presence of children?

If the wife is in a relationship with someone other than her husband, she must repent and desist from these grave sins. If the husband does not provide for her chastity or is consistently unable to have intercourse with her, and she fears temptation for herself, she has the right to seek a divorce (ṭalāq) or an annulment through khulʿ by offering financial compensation. The husband must accept this. If he refuses, she can take him to court to compel him to fulfill what is legally required.