Praise be to Allah.
When a Muslim is able to do Hajj, he should hasten to do it, and it is not permissible for him to delay it for no reason, because the Prophet (peace and blessings of Allaah be upon him) said: “Hasten to do Hajj – i.e., the obligatory Hajj – for none of you knows what will happen to him.” (Narrated by Ahmad, 2721; classed as saheeh by al-Albaani in al-Irwa’, 990). And he (peace and blessings of Allaah be upon him) said: “Whoever wants to do Hajj, let him hasten to do so.” (Classed as hasan by al-Albaani in Saheeh Abi Dawood, 1524).
What you have mentioned about your brother’s problems is not a reason for delaying Hajj, because Hajj will not prevent him from dealing with this problem, since it is within his power to try to solve this problem and finish with it before he goes for Hajj. His Hajj may be the means of his problem being solved, because of the help from Allaah it may bring and the blessing (barakah) of Hajj and obedience to Allaah. It may be that he will make du’aa’ during his Hajj with regard to this matter, and Allaah will answer and relieve him of this distress.
Moreover, our advice to your brother is that he should not hasten to divorce his wife, rather he should take his time and not rush into anything. For divorce is something that Allaah dislikes.
If the problem between him and his wife is because of negligence on her part regarding one of the duties towards Allaah, such as if she neglects to pray or is not chaste, etc, then he has to warn her and remind her about Allaah, and call her to Allaah, and try to guide her to obey Allaah. If she persists in not responding to him, then in that case there is nothing to be gained by keeping her.
But if the problem between them is of the common type of problems between spouses, and has to do with differences of opinion concerning day to day life and household matters, etc., then he has to be patient and treat her kindly, and try hard to correct what he thinks is inappropriate. For Allaah says (interpretation of the meaning):
“and live with them honourably. If you dislike them, it may be that you dislike a thing and Allaah brings through it a great deal of good”
The husband has to live with his wife honourably and keep her company in a good way, refraining from harming her, and treating her kindly. Living with her honourably also means putting up with any annoyance that his wife may cause him, and he should remember that he will have a great reward for that from Allaah.
A man may dislike his wife, but he keeps her out of obedience to Allaah and treats her kindly, and then Allaah brings about a great deal of good from that. He may be blessed with righteous children from her who will benefit him in this world and in the Hereafter; or his dislike may be taken away and replaced with love, as often happens.
The Messenger (peace and blessings of Allaah be upon him) said: “No believing man should hate a believing woman; if he dislikes one of her characteristics he will be pleased with another.” (Narrated by Muslim, 1469). What this means is that it is not appropriate for a believing man to hate a believing woman, because even if he finds some bad characteristic in her for which he may dislike her, he will find another, praiseworthy, characteristic for which he will love her, such as her being chaste or kind or obedient, or some other good characteristic. The same is true of all people, each person has some good attributes and some bad attributes. As the poet said:
“Who is there that is pleasing in all his characteristics? It is enough honour for a man’s faults to be few enough to count.”
The wise man is the one who weighs up both the good characteristics and the bad.
Your brother should make a lot of du’aa’ in the places and at the times when du’aa’ is especially encouraged, during Hajj and otherwise, asking that Allaah may reconcile him with his wife and create love between their hearts.
And Allaah knows best. May Allaah bestow blessings and peace upon our Prophet Muhammad.