Will a man be held accountable for not desiring to have children due to marital problems and a strained relationship with his wife, despite their religiosity and the fact that they already have two children?

He must try to reconcile with his wife by acting wisely, being a good role model, and continuously advising and admonishing her, accompanying this with good deeds. If these means do not succeed, then he should add lawful abandonment, prevent her from harmful relationships, and he can marry another if he is able. He must also fear Allah and fulfill His rights. As for not having children, that is not a solution and may lead to greater harm.