It is not obligatory for a husband to bear the costs of his wife’s Hajj, even if he is rich. Rather it is mustahabb for him to do so and he will be rewarded for that, but he is not sinning if he does not do that.
That is not enjoined by either the Qur’aan or the Sunnah. But Islam gives the wife the Mahr which is her exclusive right, and it permits her to dispose of her own wealth.
Rather Islam enjoins on the husband to spend on his wife in a manner that is good and reasonable, but it does not oblige him to pay off her debts, or to pay zakaah on her behalf, or to pay the costs of Hajj etc.
Shaykh Ibn ‘Uthaymeen was asked: will a husband be rewarded if he appoints someone to do Hajj on his wife’s behalf, if she dies without having done Hajj?
He said: it is better for him to do Hajj on her behalf himself so that the rituals will be done properly… Then he said: But as for it being obligatory, that is not obligatory for him.
Al-Liqa’ al-Shahri, 34, no. 579
Just as it is not obligatory to make up Hajj on her behalf after she dies, so too it is not obligatory for him to pay for her Hajj whilst she is still alive.
This is as far as the issue of whether or not it is obligatory is concerned. With regard to being kind to her, if he does that then Allaah does not cause the reward of those who do good to be lost, and Allaah will record for him the reward of her Hajj.
The fuqaha’ (may Allaah have mercy on them) stated that it is obligatory for a husband to spend on his wife’s Hajj in the event that he deliberately spoils her Hajj, such as one who forces his wife to have intercourse before the first stage of exiting ihram, etc.
Shaykh ‘Abd al-Kareem Zaydaan said:
It is not one of the wife’s rights over the husband that he should bear the costs of her Hajj, or share the costs with her.
Al-Mufassal fi Ahkaam al-Mar’ah, 2/177
Shaykh al-Albaani (may Allaah have mercy on him) was asked about the same issue and he replied: It is not obligatory for a husband to pay the expenses of his wife’s Hajj. This has to do with men. If a woman has sufficient money to go for Hajj then it is obligatory for her to go for Hajj; if she does not have enough money then she is not obliged to go for Hajj.
And Allaah knows best.