Is a woman entitled to seek separation from her husband who abandons her for long periods, especially after his repeated marriages to maids and his neglect of her and their children, and is she considered sinful if she refuses intimacy with him in the event that he has abandoned her for many months?

What a husband does by not being just between his two wives is forbidden and incurs Allah's wrath, for justice between wives in division and lodging is an obligation. However, it is absolutely not permissible for the wife to request separation, nor to expel her husband from his house, nor for her to leave his house, nor to refuse to share his bed, as these matters are forbidden. But if the husband persists in his injustice and lack of fairness, then the wife may request a divorce due to his dereliction of her right.